Beautiful Cycles: A Theory and a Model Implying a Curious Role for Interest*

Marco Gross

doi:10.5089/9781513571676.001.A001

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Beautiful Cycles: A Theory and a Model Implying a Curious Role for Interest^*

Author: Mr. Marco Gross¹

¹ 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Contributor Notes

Author’s E-Mail Address: mgross@imf.org

Publication Date:: 05 Mar 2021

eISBN:: 9781513571676

Language:: English

Keywords:: Business and financial cycles.; WP; firm profits; price inflation; profit share; interest rate; market power; money stock; firm profit share; inventory management; data-based analysis; Interest coverage ratios

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Where do economic cycles come from? This paper contemplates an utmost minimalistic model and underlying theory that rest on two assumptions for letting them emerge endogenously: (1) the presence of interest-bearing debt; and (2) a degree of downward nominal wage rigidity. Despite its parsimony, the model generates well-behaved, self-evolving limit cycles and replicates six essential empirical facts: (1) booms are long- while recessions short-lived; (2) leverage is procyclical; (3) firm profit and wage shares in GDP are counter- and procyclical, respectively; (4) Phillips curves are downward-sloping and convex, and Okun’s law relation is replicated; (5) default cascades arise endogenously at the turning points to recessions; (6) lending spreads are countercyclical. One can refer to the model as being of a Dynamic Stochastic General Disequilibrium (DSGD) kind.

Abstract

1. Introduction

Business cycles are cycling in a regular, far from purely stochastic manner. Figure 1 illustrates this for the US. Theory throughout the 20^th century in the field of New Classical economics—real business cycle (RBC) theory (Kydland and Prescott 1982) as a sub-branch—as well as New Keynesian (NK) models and mixtures of the two (DSGE models following the New Consensus, since Goodfriend and King 1997 and Clarida et al. 1999), sought such behavior’s source in random shocks. Disequilibrium theory ensuing Keynes with Kalecki (1935/37), Kaldor (1940), Goodwin (1951/67), and Minsky (1975/86), aims to explain such dynamics through endogenous, self-evolving economic forces. System dynamics models (SDMs) represent one stream of nonlinear aggregative models to model disequilibrium processes (references follow in Section 2). Their drawbacks include that their dynamic behavior is sensitive to chosen functional forms and that they do not contain individual agents, for defaults of agents to be ruled out by design. Agent-based models (ABMs, LeBaron and Tesfatsion 2008) are an appealing alternative methodology for various reasons, including for the easy allowance of agent defaults. Macro-financial ABMs—despite being insightful—tend, however, to combine so numerous behavioral assumptions in one go. This disguises the root causes for cycles to emerge, opposed to factors that amplify or dampen them.

Against this backdrop, the objective of this paper is three-fold: (1) to develop a model and underlying theoretical rationale that generate endogenous cycles based on a most minimal set of assumptions, avoiding complexity by all means; (2) to delineate what pre-conditions for cycle emergence are, opposed to what amplifies or dampens cyclical behavior once present; and (3) to promote the use of stock-flow consistent ABM methodologies. The model in Section 3 is surrounded by a literature perspective in Sections 2 and 4, for relating it to existing SDMs, ABMs, sources of cycle amplification and dampening, and to the work of Hyman Minsky.

Despite its simplicity, the model generates self-evolving cycles and replicates six empirical facts. These include: (1) booms are long- while recessions short-lived; (2) leverage is procyclical; (3) firm profit shares and wage shares in GDP are counter- and procyclical; (4) wage and price Phillips curves are downward-sloping and convex, and Okun’s law is replicated; (5) default cascades arise endogenously at the turning points from expansions to recessions; (6) lending spreads are countercyclical. All this macro behavior from the model emerges endogenously “from the bottom up.” GDP growth and unemployment rates from the model exhibit fat tails (excess kurtosis) as in the data for the US and other countries.

The model can be seen as a theoretical grounding for the Growth-at-Risk (GaR) framework (Adrian et al. 2019). Its rationale—which GaR captures in an econometric fashion—has much in common with the endogenous cycle narrative presented here, and in turn with Minsky as well. Moreover, the model here rests on a strong demand-oriented propagation mechanism compatible with the business cycle “anatomy” conceived by Angeletos et al. (2020). The model’s narrative and quantitative behavior squares as well with the work of Schularick and Taylor (2012) and Jorda et al. (2013/15/16a) who document the empirically strong relationship between credit and real economic activity.

The paper concludes: The root causes of cyclical behavior can be seen in lying in (1) the presence of interest-bearing debt; and (2) a degree of downward nominal wage rigidity; which, respectively, reflect institutional and behavioral reality and serve to micro-found the model. The theory’s related implication is that interest generates firm profits, a precondition for which, in turn, is debt-financed investment. Various amplification and dampening mechanisms are discussed in Section 4, where four accelerator types are defined: a collateral, mispricing, policy, and herding accelerator. The model codes are made available along with this paper.

2. Literature

This section motivates which ingredients the model subsequently set up in Section 3 ought to comprise. These concern the choice of a model methodology that allows for disequilibrium dynamics to emerge (Section 2.1), the relevance of downward nominal wage rigidities (Section 2.2), and a perspective on existing ABMs (Section 2.3).

2.1 Equilibrium and Disequilibrium Theory

Twentieth century economic theory can be partitioned into an equilibrium and disequilibrium strand. Equilibrium theory is rooted in Neoclassical Economics of the early 1900s, splitting into New Keynesian and New Classical streams, with RBC theory as a New Classical branch parallel to Monetarism.¹ Concerns about RBC and DSGE models are mounting: (1) in what they miss, inter alia, regarding incomplete markets, imperfect competition, endogenous money, and behavioral aspects; and (2) in what sense they are distorted more fundamentally, for example, regarding the rational expectations assumption and the representative agents paradigm. Kirman (1992), Akerlof (2002), Mankiw (2006), Howitt (2012), Blanchard (2016a/b, 2017), Stiglitz (2011/17), and Haldane and Turrell (2018) are some of those who explicate such concerns in detail.

In parallel, disequilibrium theory emerged since the early 20^th century. A “pure” monetary theory of business cycles assigning a central role to credit was presented by Hawtrey (1919). The role of innovation for driving business cycles was conceived by Schumpeter (1912), explaining the emergence of cycles through the clustered occurrence of innovative firms. A series of research then emerged following the work of Keynes (1930/36), which served to anchor the ensuing endogenous business cycle (EBC) literature starting with Kalecki (1935/37), Harrod (1939), Kaldor (1940), and Goodwin (1951/67).

The disequilibrium theory stream widely acknowledges that money is endogenous. Money is created through bank lending, as a function of demand and with supply being bound by regulation, constraining bank leverage on the upside (Werner 2014a/b/2016, Mc Leay et al. 2014a/b, Gross and Siebenbrunner 2019). It does not preclude the on-lending of existing money stocks resting in the system by non-bank financial and nonfinancial agents, which creates additional leverage for some agents but leaves aggregate money stocks unchanged. Mistakenly modeling banks as intermediaries results in misperceiving the impact of monetary and macroprudential policy and underestimating the role of credit. In a DSGE model context this has been emphasized by Jakab and Kumhof (2015). The endogenous money reality is well acknowledged in Post-Keynesian economics (Lavoie 2014, Hein 2017), there referred to as the Horizontalists view (Moore 1988), and reflected in the model developed here.

Minsky augmented Keynes’s theory by introducing debt for financing investment as a basis for his cycle narrative. He considered neoclassical theory flawed in its equilibrium concept and the omission of debt finance (Minsky 1975/86). He agreed with Keynes on the importance of fundamental uncertainty, that expectations matter for investment decisions, and that fiscal and monetary policies are useful to contain cycles. His financial instability hypothesis posits that the financial system induces swings between stability and fragility and that these are responsible for driving business cycles endogenously (Minsky 1986/93). His writings are inspiring, including for the model here, though in one respect he drew a misled conclusion (see Section 4.1).

A system dynamics model (SDM) stream connected to the work of Kalecki, Harrod, Goodwin, and Minsky since the 1970s. Early entry points to this literature include Torre (1977), Taylor and O’Connel (1985), Foley (1987), Semmler (1987), Asada (1989), and Jarsulic (1989);² who developed aggregate nonlinear dynamic models, usually with three to five or sometimes more differential equations. Many of them are built around the Keynesian investment accelerator, and various expand in some form on the predator-prey model structure (that is, a Lotka-Volterra system) from mathematical biology as exemplified in Goodwin (1967). Numerous of them cite Minsky to motivate the role of credit. A survey of models with Minskyan elements can be found in Nikolaidi and Stockhammer (2017). An in-depth review in Zarnowitz (1985) summarizes equilibrium and disequilibrium theories from the first two thirds of the 20^th century, commenting on p. 546 that “purely stochastic explanations have no theoretical content, and it is the factors which can be integrated in an economic theory that are naturally of primary interest to any economist who attempts to understand the nature and causes of business cycles.” Moreover, linear time series model-based impulse responses being not very persistent for various macroeconomic variables should not be misinterpreted as meaning that more persistent cyclical behavior is irrelevant, but instead that relevant nonlinearities are likely missed (Beaudry et al. 2017).

Traces of Minsky’s mindset can be found outside the Post-Keynesian literature. A supply side-oriented model connecting to Kalecki (1939) in Greenwald and Stiglitz (1993) requires firms to finance investment before production, as in the model here. Their model has an RBC flavor in not allowing for unemployment, however, while it tells a narrative of cyclical wages, output, and investment. According to Bernanke et al. (1996/99)’s financial accelerator, shocks get amplified through debt-leveraged firms and the external finance premium is countercyclical. A land collateral-based model with a predator-prey structure was developed in Kiyotaki and Moore (1997). A stylized model of portfolio investment in Bhattacharya et al. (2015) usefully motivates the emergence of countercyclical risk premia. Models with endogenous procyclical leverage can be found in Brunnermeier and Sannikov (2014) and Danielsson et al. (2012/16a/b). Similar in spirit, the Growth-at-Risk model of Adrian et al. (2019) captures the time-varying relation between real activity and financial conditions in an econometric fashion.³ None of the models referenced here generate self-evolving economic cycles, since they employ equilibrium methodologies.

2.2 Downward Nominal Wage Rigidities

Downward nominal wage rigidities can be traced to Keynes. It is a real-world fact in his view, as workers assess their wages relative to reference groups and dislike wage cuts. In his view, “whether logical or illogical, experience shows that this is how labour in fact behaves” (Keynes 1936, Ch. 2). Three streams of theory approached the topic since Keynes: a first correlates with him in assigning a role to psychological factors and fairness (Kahneman and Tversky 1979, Kahneman et al. 1986, Akerlof and Yellen 1990, Fehr and Falk 1999). It relates to the notion of money illusion (Fisher 1928, Patinkin 1965) insofar as people perceive nominal dynamics, for example, regarding wages, as more relevant than real, for psychological reasons. A second theory assigns a role to unions and collective wage bargaining (Calmfors and Driffill 1988, Lindbeck and Snower 1988, Layard et al. 1991, Booth 1994, Holden 1994). Such labor market structures can be seen as a consequence of psychological factors and, hence, this stream be regarded as sub-ordinate to the one rooted in psychology and money illusion. Third are theories on efficiency wages that see the rationale for firms paying higher than market-clearing wages in disciplining workers and sustaining their productivity (Shapiro and Stiglitz 1984, MacLeod and Malcolmson 1998).

Substantive evidence for downward wage rigidities can be found in three sub-branches of the empirical literature: (1) interview-based evidence for the relevance of downward wage rigidities through arguments of motivation, moral, and sustaining productivity can be found for the US in Loewenstein and Sicherman (1991), Campbell and Kamlani 1997, Bewley (1995/99), Shafir et al. (1997); (2) household and firm micro data-based analyses that confirm downward rigidities for the US can be found in Holzer and Montgomery (1993), Card and Hyslop (1997), Kahn (1997), Wilson (1999), Altonji and Devereux (2000), Lebow et al. (2003), Daly and Hobijn (2014); for Switzerland in Fehr and Goette (2005), and for Germany, Italy, and the UK in Goette et al. (2007); and (3) supportive macro time series-based analyses, using industry- or economy aggregate-level data, can be found for the US in Ghali (1999), Mehra (2000), and Banerji (2005), for Switzerland in Zanetti (2007); for 19 OECD countries in Holden and Wulfsberg (2008); and for Germany, France, Spain, and Italy in Bobeica et al. (2019). Wages are found to Granger-cause prices and the relation between them to be stronger at times of high inflation (booms), thereby supporting the hypothesis of downward rigidities. These findings conform with the Post-Keynesian cost-push view as well, unlike in neoclassical theory, where prices drive wages. Empirical evidence for downward wage rigidities being so numerous for the US, despite union and collective bargaining being far less prevalent, implies that psychological factors appear to determine wage dynamics even without such structures in place.

The theory streams on wage formation feed into the question of the shape of the Phillips curve (Phillips 1958) and more empirical literature whose findings square with downward wage rigidities. Regardless of their origin, downward wage rigidities would be a source of convexity in the Phillips curve (Fisher 1989, Akerlof et al. 1996).⁴ Other possible explanations for convexity in Phillips curves include capacity constraints (Macklem 1997, Dupasquier and Ricketts 1998). Empirical evidence for a convex Phillips curve shape is extensive: see Kumar and Orrenius (2015), Ball and Mazumdar (2011), and Huh and Jang (2007) for recent evidence for the US. Some 15 additional references supportive of convexity in the US Phillips curve are collected in Gross and Semmler (2019), alongside numerous additional ones for European and other countries.⁵

2.3 Macro-Financial ABMs

Early ABMs focused on firm distributional aspects and firm entry-exit dynamics. Delli Gatti et al. (2003/05) included elements of debt finance following Minsky and put forward the network-based accelerator through correlated firm defaults (Delli Gatti et al. 2010). These models were not yet built on stock-flow consistency principles, did not include a role for wages and price dynamics, and did not allow for defaults of agents. I interpret them as a bridge between SDMs and stock-flow consistent ABMs.⁶

A second macro ABM chain started adding elements of inventory management, target capital levels, and expectation formation rules for investment in Dosi et al. (2006). Their model structure reflects Keynesian multiplier and accelerator effects, the latter through adaptive demand expectations which drive investment, and not allowing for defaults. Dosi et al. (2006) and their follow-up model variants (Dosi et al. 2010/13/17) model wages as a function of goods price inflation, labor productivity, and unemployment. Their focus is on replicating basic stylized facts: investment (consumption) is more (less) volatile than output, investment and consumption are procyclical, and investment is influenced by firms’ financial structure. Keynesian stabilization policies are seen to reduce output volatility (Dosi et al. 2010) and regarded as complementary with Schumpetarian innovation (Dosi et al. 2017).

The Eurace model stream forms a third ABM cluster. The Eurace model stream started with Dawid et al. (2008/09) and Deissenberg et al. (2008), as part of an EU-funded project initiated in 2006 involving academics from France, Germany, Turkey, and the UK.⁷ The Eurace model structure is quite massive, including, inter alia, complementarities between the quality of capital and employee skills, multi-round search and matching in the labor market, differentiated and endogenously evolving skills for workers, inventory planning, mark-up pricing, stocks and bond markets, governments that operate a tax and unemployment benefit scheme, buffer-stock savings behavior for households, firm equity issuance, spatial sub-regional structures, and wage formation structures that let employers’ expectations about workers’ skill level influence salaries.⁸

Other ABMs have evolved in parallel with these three streams. Chiarella and Di Guilmi (2011) link the valuation of capital assets to a stock market, where investors have heterogeneous expectations about firms’ future profits. Prices are set as a mark-up over wages and wages set flexibly so that product markets clear. An extension of Delli Gatti et al. (2010)’s firm network-based accelerator in Riccetti et al. (2013) adds a variable leverage target mechanism for firms, which was further augmented with a dynamic trade off theory-based capital structure in Riccetti et al. (2015). Countercyclical capital rules stabilize the economy but lose their effectiveness when combined with interest rate policy (Alexandre and Lima 2017), where interest rate smoothing is seen to be beneficial. A triple mandate Taylor rule with credit growth next to an output and inflation gap performs best in stabilizing the economy in Popoyan et al. (2017), where wages are linked to prices and involving firm inventory management. Extended with an interbank market (Popoyan et al. 2020), interbank market freezes arise endogenously and the Basel III LCR spurs instability, as it may increase the procyclicality of reserves. ABMs are also shown to have the potential to outperform DSGE and time series model-based forecasts (Poledna et al. 2021). Very useful bird’s-eye-view papers on macro ABMs and their use for policy analysis so far can be found in Fagiolo and Roventini (2017), Hommes and LeBaron (2018), and Dosi and Roventini (2019).

Seeing the model developed here in perspective: it follows a stock-flow consistent integrated balance sheet approach, as in the Eurace model family and others.⁹ It is in line with the Dosi et al. and the Eurace models in allowing wages to be a function of price inflation, but simplified in assuming constant labor productivity and augmented by having a downward wage rigidity. The Eurace models and others appear to be very comprehensive regarding agent types, markets, and behavioral features. This implies a disadvantage: one cannot easily explain the model dynamics or easily trace the root causes of cycles as opposed to mechanisms that amplify or dampen them.¹⁰ Against this background, the aim is to develop an utmost parsimonious ABM, which, despite its simplicity, generates well-behaved cyclical behavior and replicates a rich set of stylized facts in a way not seen in the literature, to the best of my reading.

3. Model and Simulations

3.1 The Model

The model has three agent types: firms, households, and a banking system. Tables 1 and 2 show their integrated balance sheets and the net worth-non-neutral financial flows across agents. Figure 2 shows the sequence of the agents’ (inter-) actions during one time period. The model has multiple firms (f = 1... F) because explicit default on their debt will want to be allowed. Hence, assuming a representative firm sector is not an option, as the sector’s default would imply for the whole economy to crash. Having many firms means that multiple households (n = 1... N, N > F) are needed, as they work at the firms. The banks can be compressed to one banking system since the results will not depend on having one or many banks; thereby adhering to the “reduce complexity by all means” approach. The money creation ability, through granting credit to firms in the model, is no different in a one-bank or multi-bank system.¹¹

^{Table 1.}

Agents’ Integrated Balance Sheets

^{Table 1.}

Agents’ Integrated Balance Sheets

	Assets	Liabilities
Firms (f=1…F)	M_f: Money holdings, deposited at bank	L_f, Loans
Firms (f=1…F)	M_f: Money holdings, deposited at bank	E_b, Net worth
Households (n=1…N)	M_n: Money holdings, deposited at bank	E_n, Net worth
Banking System	sum(L_f): Loans to firms	sum(M_f)+sum(M_n): Households’ and firms’ money holdings
Banking System	sum(L_f): Loans to firms	E_b, Net worth

^{Table 1.}

Agents’ Integrated Balance Sheets

	Assets	Liabilities
Firms (f=1…F)	M_f: Money holdings, deposited at bank	L_f, Loans
Firms (f=1…F)	M_f: Money holdings, deposited at bank	E_b, Net worth
Households (n=1…N)	M_n: Money holdings, deposited at bank	E_n, Net worth
Banking System	sum(L_f): Loans to firms	sum(M_f)+sum(M_n): Households’ and firms’ money holdings
Banking System	sum(L_f): Loans to firms	E_b, Net worth

^{Table 2.}

Agent Net-Worth Non-Neutral Financial Flows Across Agents

^{Table 2.}

Agent Net-Worth Non-Neutral Financial Flows Across Agents

		Recipient
		Firms	Households	Banking System
Sender	Firms	–	Wages (w)	Debt interest payments (a^I)
	Households	Consumption expenditure (c)	-	-
	Banking System	-	Dividend payout (div)	-

^{Table 2.}

Agent Net-Worth Non-Neutral Financial Flows Across Agents

		Recipient
		Firms	Households	Banking System
Sender	Firms	–	Wages (w)	Debt interest payments (a^I)
	Households	Consumption expenditure (c)	-	-
	Banking System	-	Dividend payout (div)	-

The base version of the model operates with credit money only. There is no “off-the-leash,” debt-free (outside) money in circulation. Firm and household money stocks, created endogenously through debt, are held in electronic form at the banking system’s deposit pool (Table 1). The total money stock is defined to equate to the size of the banking system balance sheet, hence to outstanding loans, as “off-the-leash” money is zero for now. It includes banks’ net worth by convention here, for loan interest payment flows to the bank to not imply money destruction.¹² Net worth neutral financial flows include principal debt issuance (money creation) here for firms, and principal debt repayment (money destruction). These flows are not depicted in Table 2, as it is confined to flows that change the agents’ net worth.

Step 1: Wage setting. Active firms set nominal wages ahead of a forthcoming production round. The logic to reflect a downward nominal wage rigidity entails that firms align wage growth for the forthcoming production round by indexing wages to recent price inflation if their profits were trending up from t-2 to t-1 and if price inflation in t-1 was positive. If their profits trended down or price inflation was negative, they keep nominal wages flat. Defining wage per employee growth at the active firm-level as $w_{t, f}^{g} = w_{t, f} / w_{t - 1, f} - 1$ , this logic in equation form reads as:

\begin{matrix} (1) & w_{t, f}^{g} = {\underset{0}{p_{t - 1, (f)}^{g}} w h e n \underset{o t h e r w i s e}{p_{t - 1, (f)}^{g} > w_{t - 1, f}^{g} & p_{t - 1, (f)}^{g} > 0}} \end{matrix}

where $p_{t, f}^{g} = p_{t, f} / p_{t - 1, f} - 1$ denotes goods price inflation. Firms and households, jointly as a matter of interpretation, thereby form price inflation expectations in an adaptive manner. Firms measure the previous period’s price growth either with reference to their own firm f or the economy-wide aggregate. If computed at the economy level, it is done for the subset of firms that were active in t -1 and t -2. Firms that were inactive in t-1 set the forthcoming wage per employee in t to the average of the active firms’ wages in t-1. At the outset in t = 1, all firms are set to be active and the initial wage per employee is set to an arbitrary nominal value for all firms. The model dynamics do not depend on this initial value. In period t = 2, wage and price growth as of t = 1 cannot be computed yet, for contractual wages to still stay at their t = 1 level. From period t = 3 forward, equation (1) is applied by each firm. The implication of the overall wage setting structure for the system behavior is explored in Section 3.3.

Step 2: Loan granting. New loans are granted to active firms in case they face a shortfall between the forthcoming wage bill and their current cash stock. This, by design, is the case in period t = 1, when no money is contained in the system yet and the wage bill is implied by the number of workers times the initial nominal wage per employee set in Step 1. Firms’ cash stocks can be positive but insufficient to cover a forthcoming wage bill, in which case their debt is “topped up.” They can be larger than the wage bill, in which case no additional credit is requested. The loans can be interpreted as working capital loans or loans for investment alike. This difference in interpretation is semantic in the model; a related discussion follows in Section 4.1. A loan pricing equation is designed for the effective interest rate to equate a loan’s expected interest income net of funding costs $(i_{t}^{d})$ with its expected loss (PD_t x LGD_t), and adding a profit margin μ:

\begin{matrix} (2) & \underset{Rxpected Loss}{\underset{︸}{P D_{t} \times L G D_{t}}} + \end{matrix} \underset{Expected Interest Expenses}{\underset{︸}{(1 - P D_{t}) (μ + i_{t}^{d})}} = \underset{Expected Interest Income}{\underset{︸}{(1 - P D_{t}) i_{t}}} \leftrightarrow i_{t} = μ + i_{t}^{d} + \frac{P D_{t} \times L G D_{t}}{1 - P D_{t}}

The funding cost $i_{t}^{d}$ is set to zero still in the base model version. The probability of default (PD) is measured through realized default flows; the loss given default (LGD) involves the defaulted loans’ recovery value:

\begin{matrix} (3) & P D_{t} = \frac{Σ_{f}^{F} D e f a u l t F l o w_{f, t}}{L_{t - 1}} a n d L G D_{t} = \frac{Σ_{f}^{F} [D e f a u l t F l o w_{f, t} - \min (D e f a u l t F l o w_{f, t})]}{Σ_{f}^{F} D e f a u l t F l o w_{f, t}} \end{matrix}

Defaulted loans are written off immediately, so that nonperforming loan (NPL) stocks do not build up. There is no consideration of leverage constraints à la Basel, as it is not required for generating the model dynamics. There is no interest rate-based monetary policy reflected in the model yet; with the base rate being constant and equal to μ.

Step 3: Active firms pay wages. Wage payments flow from active firms to their employees’ deposit accounts. Firms’ net worth is reduced, households’ net worth increased, and the banking system’s net worth unaffected by these transfers.

Step 4: Production, price setting, and sales. Production is accomplished based on labor input, with constant labor productivity. A firm having N_f = N/F workers hence either produces N_f real output units when active or 0 when being inactive after a default arose in a previous period (in Step 6):

\begin{matrix} (4) & y_{f, t}^{r e a l} = N_{f}, \forall f \in a c t i v e \end{matrix}

Households with a positive cash balance choose at random one firm from the active firm subset and communicate the amount, $c_{n \to f, t}^{n o m}$ , they plan to spend. Firms in turn set the unit price, P_f,t, so that all the communicated amount, summed across the relevant households, is received as sales revenue, thereby maximizing firm profit and not requiring any inventory or scrapping of real output:

\begin{matrix} (5) & p_{f, t} = \frac{c_{n \to f, t}^{n o m}}{y_{f, t}^{r e a l}}, \forall f \in a c t i v e \end{matrix}

This pricing equation implies that supply shocks (if they were to be considered, for example, through a productivity parameter in eq. 4) result in conventional sign-opposite output-price responses (Blanchard 1989). Nominal consumption, $c_{n, t}^{n o m}$ , amounts to the wage received in the same period (Step 3):

\begin{matrix} (6) & c_{n, t}^{n o m} = w_{n, t -}^{n o m} \end{matrix}

where the within-period time lag is denoted by “t -” in the subscript to the wage flow variable. Households thereby do not accumulate money holdings across time increments yet, but only momentarily within a period, between wage receipt and consumption. There is a built-in price-wage dependency via the flow-consistent nature of the model. Wages are paid first (Step 3); prices are implied by households spending the wage income subsequently (Step 4). Prices are persistent to the extent that wages are sticky through having wage contracts in place.

Step 5: Banks pay dividends. The banking system pays dividends div_t whenever its capital ratio, CAR = NW/L, surpasses a self-defined threshold, CAR^tar.

\begin{matrix} (7) & d i v_{t} = \max (0, (C A R_{t - 1} - C A R^{t a r}) L_{t}) \end{matrix}

The dividend flows in equal shares to households’ deposit accounts, thereby adding to their consumption spending in the following period. It subtracts from the banking system’s net worth for its capital ratio to drop to target. Deposit rates are zero for now, without loss of generality of the model dynamics.

Step 6: Debt service. Debt-holding firms pay their full annuity if their cash stock suffices to do so. Principal debt is rolled over if a firm is not able to pay the full annuity, but only interest, in which case it does pay only interest. If a firm is not able to pay the full interest (partial coverage of interest is not allowed), it defaults and is “inactive” for the following, one period. In this case, its principal debt is written off the bank and firm balance sheet, and the bank attempts to recover the debt by seizing the defaulted firm’s remaining cash balances. Importantly, defining default in this way (no borrowing to cover interest) means that there is no Ponzi finance possible by design. An inactive firm does not pay wages in the period in which it is inactive. Its assigned workers are recorded as unemployed until they become active again, the period after inactiveness. After Step 6, the end-of-period balance sheet position of all agents is recorded and set as the starting point for the next period, following a next round of stock-flow consistent transactions across agents.

3.2 Base Simulation and Economic Cycle Narrative

The base simulation. The profit margin for banks was set to μ = 0.05 and the target capital ratio beyond which banks pay out dividends is set to 10 percent.¹³ A base simulation was conducted with F = 200 firms, N = 20,000 households, and T = 30,000 periods; the first 800 periods are shown in Figure 3. The price and wage Phillips curves are downward sloping and convex, and Okun’s law relation is obtained (Figure 4).

In t = 0, the economy stands still, and all agents’ balance sheets are “empty”, having zero money (debt) in the system. In period t = 1, the economy is actuated by defining a first wage bill (Step 1) and firms obtaining a first round of corresponding principal debt to cover the bill (Steps 2 and 3). The consumption expenditure flows in a stochastic manner in terms of firm choice back to the firms (Step 4), while the full initial principal influx returns as a firm sector sales revenue from an economy-wide viewpoint. The economy-wide sales revenue would suffice to repay precisely all principal, but not the interest. At the firm-level, due to firm choice stochasticity, some firms might be able to cover also interest, while others would not. Principal debt is rolled over if only interest can be covered (Step 6). Interest coverage ratios (ICRs) are defined as cash stocks before interest payments over interest payments. Firm profits are measured as sales revenue minus the wage bill. The following description of the cyclical dynamics all refers to Figure 3.

Boom times. The addition of principal interest-bearing debt implies a slowly rising debt stock, for firms to cover the loan interest. Whenever principal debt for a firm is rolled over, the earnings before interest generally well suffice to cover the interest; there prevails, though, a small level of frictional unemployment, reflective of a few firms being inactive due to their default, also during boom times. The downward wage rigidity meanwhile induces an upward momentum in the leverage process. Debt being interest-bearing implies that more principal debt keeps being added to the system for firms to cover their contractually set wage bill, which banks provide as firm profits and ICRs appear solid, supported by the continual influx of principal debt. The ICRs meanwhile slowly deteriorate. Firm profit shares slowly decrease, and mirror-wise, wage shares slowly increase. Whenever the banking system has accumulated a sufficiently high capital ratio, it pays dividends (or effectively equivalently, interest on deposits). This is when the household sector can spend more than what it receives through wages, and it is when profits at the aggregate level can become positive and positive price inflation occur. In any subsequent period of such a price rise, wage inflation follows suit, spurring the price-wage process and a related stronger pull for some more principal debt by firms whose cash stock after sales does not suffice to cover the next wage bill.

The interest income for the household sector as a source for firm profits is essential. It can be seen by relating the two from the base simulation and opposing it to US data over a 28-year period since 1992 (Figure 5). It is interesting to see not only the positive correlation in the US data, but the quantitative approximate correspondence between firm profit flows and household interest income. The household sector interest income and firm profits would not equate perfectly, for various reasons; these include that a faster savings (dissaving) process from standing household savings stocks can drive firm profits temporarily down (up). Savings ratios in the US appear rather stable historically.¹⁴ A related experiment, allowing for household savings, follows later.

The turning point. The aggregate debt stock and related interest burden have grown so high, and firms’ interest coverage ratios become so thin, that any small perturbation makes a first firm unable to cover its interest payments and hence default. The perturbation can be (1) a small interest rate rise, for example, resulting from further contracting monetary policy (not in the model yet)—which is not meant to induce a downturn, though it would—or a slight rise in risk premia; or (2) a small perturbation in demand, in relative terms due to stochastic firm choices or absolute in terms of firms or households saving more momentarily. In the base model, it is the relative demand disturbance through stochastic firm choice. Any external factor can induce such interest or demand fluctuations, which are the two fundamental channels through which any perturbation is induced at a turning point. They might be large, but it would suffice if they were small. They would be as unnoticeable as always but have the potential to induce the cycle to turn due to the system being so “stretched” (highly leveraged) at this juncture.

The downturn. The default of one or a small set of firms at the turning point induces a default cascade through various channels. First, the spending potential of those agents who became unemployed at the turning point falls, making them spend less at other firms that did not default at the turning point yet but now tend to default as well, as the entire firm population is rather highly indebted. This channel mirrors the one that Guzman and Stiglitz (2020) refer to as the “income effects as the consequence of bankruptcy.” Second, in parallel, rising loan interest rate risk spreads make firms’ interest burden increase further, implying the materialization of more defaults, independent of the demand effect. These two most fundamental channels are captured in the model. Yet other amplification channels are discussed in Section 4.

The new upturn. After enough firms have defaulted and their debt has been written off, the realized risk-based interest rate spread has fallen enough for a new debt accumulation process to start endogenously.

Six stylized facts are replicated by the model despite its high simplicity: (1) booms are long- while recessions short-lived; (2) leverage is procyclical; (3) firm profit and wage shares in GDP are counter- and procyclical; (4) wage and price Phillips curves are downward-sloping and convex, and Okun’s law relation is replicated (Figure 4); (5) default cascades arise endogenously at the onset of recessions; (6) lending spreads are countercyclical. GDP growth and unemployment rates from the model exhibit excess kurtosis: 1.4 and 3.9 (in excess of 3), compared with the corresponding kurtosis estimates based on US data equaling 2.2 and 3.4; see Fagiolo et al. (2008) for empirical evidence on excess kurtosis in macro data. RBC and NK models are known to not be quite able to generate fat-tailed distributions (Ascari et al. 2013).

Profit shares in the US data (Figure 1) attain a local peak and start falling some quarters ahead of recessions. This “phase shift” is not entirely replicated by the model yet, but only the countercyclical behavior of profit shares during the later phase of a boom. A nonlinear price-wage pass-through, to reflect time-varying, state-dependent rigidities (beyond the regime-conditional linearity assumed here), could be one mechanism that could generate such behavior. Empirical evidence to support such state dependence would first have to be devised as an empirical micro foundation, however.

3.3 Structural Experiments

Ten structural experiments were conducted to further understand the model economy’s dynamics. Table 3 shows a summary. A Fourier transform has been employed to compare the cycle frequency and amplitude based on the simulated unemployment rate under the base simulation and the various experiments. Applying the transform to other variables resulted in the same appearance of the power spectrum and hence the conclusions. The various structural experiments are referred to as “counterfactuals” in the charts throughout this section.

^{Table 3.}

Structural Experiments—Observations Relative to Base Simulation

^{Table 3.}

Structural Experiments—Observations Relative to Base Simulation

Category	#	Experiment	Cycles	Active firms and unemployment	Debt to GDP	Nominal and real GDP growth	Wage and price inflation	PD, LGD, lending spread, and ICR	Bank and firm capital ratios	Wage and profit shares	Price and wage Phillips curves
Credit	1	No credit (outside money only)	Gone	Less active firms, higher unemployment	Zero	Lower NGDP growth, RGDP growth somewhat less volatile	Price inflation lower and less volatile, wage inflation lower	All zero	Zero for banks, 100% for firms	Wage share 100%, profit share 0%	Both still downward-sloping, though location shifted
Credit	2	Initial outside money stock (endogenous credit provision subs.)	No change	No change	No change	No change	No change	No change	No change	No change	No change
Interest	3	Zero lending rate	Gone	All firms active, full employment	Unchanged regarding mean initially, but not cyclical anymore	Stochastic/explosive nominal GDP, real GDP growth flat at zero	Stochastic/explosive	All zero	Zero for both banks and firms	Wage share 100%, profit share 0%	Non-existent due to full employment at all times
Interest	4	Zero risk spread (constant lending rate)	Frequency higher, amplitude much lower	More active firms, lower unemployment	Higher	NGDP growth about unchanged, RGDP growth less volatile	Left tails less deep	PD lower, LGD unchanged, risk spread zero by design, ICR less volatile	Less deep tails for banks, higher for firms	Smaller variance	Both still downward-sloping, though location shifted accordingly with smaller range of unemployment
Wage formation	5	Downward wage rigidity off	Gone	All firms active, full employment	Stabilizes at about 110%	NGDP growth persistent and surpassing 40%, RGDP growth 0%	Both persistent and surpassing 40%	PDs and LGDs zero, ICR higher and less volatile	Both much less volatile	Approaching 100% and 0%, respectively	Non-existent due to full employment at all times
	6	Set price inflation to 20%–80% mix of firm own and aggregate	Frequency increasing, cycle duration becoming more dispersed	Less active firms, higher unemployment	Lower	NGDP growth lower, RGDP growth less volatile	Both smaller and less volatile	PDs, LGDs, and risk spreads higher, ICRs lower	Bank CAPR lower, firm CAPR higher	Wage share higher, profit share lower	Both becoming less steep
	7	Price inflation reference set to economy aggregate	Frequency very high (appearance stochastic)	Less active firms, higher unemployment	Lower	NGDP growth lower, RGDP growth rather unaffected	Both much smaller and less volatile	PDs, LGDs, and risk spreads higher, ICRs lower	Bank CAPR lower, firm CAPR higher	Wage share 100%, profit share 0%	Both flattening out (becoming horizontal)
Other	8	Loan duration larger one period	No change	No change	No change	No change	No change	No change	No change	No change	No change
	9	Directed consumption	Gone (no stochasticity)	All firms active, full employment	Stable at about 120%	Stable at 0%	Both stable at 0%	PDs, LGDs, and risk spread all zero, ICR stable at 17	Bank (firm) CAPR stable at 15% (-18%)	Wage share stable at 94%, profit share stable at 6%	Non-existent, due to full employment at all times
	10	Households save	No change	No change	Higher	No change	No change	No change	Bank (firm) CAPR higher and lower, respectively	Wage share higher, profit share lower	Slopes unchanged

^{Table 3.}

Structural Experiments—Observations Relative to Base Simulation

Category	#	Experiment	Cycles	Active firms and unemployment	Debt to GDP	Nominal and real GDP growth	Wage and price inflation	PD, LGD, lending spread, and ICR	Bank and firm capital ratios	Wage and profit shares	Price and wage Phillips curves
Credit	1	No credit (outside money only)	Gone	Less active firms, higher unemployment	Zero	Lower NGDP growth, RGDP growth somewhat less volatile	Price inflation lower and less volatile, wage inflation lower	All zero	Zero for banks, 100% for firms	Wage share 100%, profit share 0%	Both still downward-sloping, though location shifted
Credit	2	Initial outside money stock (endogenous credit provision subs.)	No change	No change	No change	No change	No change	No change	No change	No change	No change
Interest	3	Zero lending rate	Gone	All firms active, full employment	Unchanged regarding mean initially, but not cyclical anymore	Stochastic/explosive nominal GDP, real GDP growth flat at zero	Stochastic/explosive	All zero	Zero for both banks and firms	Wage share 100%, profit share 0%	Non-existent due to full employment at all times
Interest	4	Zero risk spread (constant lending rate)	Frequency higher, amplitude much lower	More active firms, lower unemployment	Higher	NGDP growth about unchanged, RGDP growth less volatile	Left tails less deep	PD lower, LGD unchanged, risk spread zero by design, ICR less volatile	Less deep tails for banks, higher for firms	Smaller variance	Both still downward-sloping, though location shifted accordingly with smaller range of unemployment
Wage formation	5	Downward wage rigidity off	Gone	All firms active, full employment	Stabilizes at about 110%	NGDP growth persistent and surpassing 40%, RGDP growth 0%	Both persistent and surpassing 40%	PDs and LGDs zero, ICR higher and less volatile	Both much less volatile	Approaching 100% and 0%, respectively	Non-existent due to full employment at all times
	6	Set price inflation to 20%–80% mix of firm own and aggregate	Frequency increasing, cycle duration becoming more dispersed	Less active firms, higher unemployment	Lower	NGDP growth lower, RGDP growth less volatile	Both smaller and less volatile	PDs, LGDs, and risk spreads higher, ICRs lower	Bank CAPR lower, firm CAPR higher	Wage share higher, profit share lower	Both becoming less steep
	7	Price inflation reference set to economy aggregate	Frequency very high (appearance stochastic)	Less active firms, higher unemployment	Lower	NGDP growth lower, RGDP growth rather unaffected	Both much smaller and less volatile	PDs, LGDs, and risk spreads higher, ICRs lower	Bank CAPR lower, firm CAPR higher	Wage share 100%, profit share 0%	Both flattening out (becoming horizontal)
Other	8	Loan duration larger one period	No change	No change	No change	No change	No change	No change	No change	No change	No change
	9	Directed consumption	Gone (no stochasticity)	All firms active, full employment	Stable at about 120%	Stable at 0%	Both stable at 0%	PDs, LGDs, and risk spread all zero, ICR stable at 17	Bank (firm) CAPR stable at 15% (-18%)	Wage share stable at 94%, profit share stable at 6%	Non-existent, due to full employment at all times
	10	Households save	No change	No change	Higher	No change	No change	No change	Bank (firm) CAPR higher and lower, respectively	Wage share higher, profit share lower	Slopes unchanged

Not allowing for credit provision lets cycles disappear, while inducing a structural rise in unemployment (Table 3, Experiment #1, Figure 6). Switching the endogenous credit provision off, and instead allowing a constant “off-the-leash” money stock to initially endow the firms, implies that fewer firms are active, that unemployment is structurally higher, and that firms cannot generate net positive profits. PDs, LGDs, risk spreads, and ICRs are zero because there is no debt. In a system with wage-contractual cash flow commitments and related downward rigidities, endogenous money serves to sustain the production flow. Endowing firms with initial outside, “off-the-leash” money and then allowing endogenous debt creation has no impact on the cycle dynamics (Table 3, Experiment #2). The role of inside money rises fast enough, during a short transitory period, for it to dominate the system behavior amid an increasingly tiny and hence negligible outside money stock.

Forcing interest rates to zero lets cycles disappear and firm profits be zero (Table 3, Experiment #3, Figure 7). Debt does arise. The debt to GDP stock-flow ratio is lower, however, than in the base simulation. Despite debt arising, there are no defaults and hence full employment. The price and wage Phillips curves are, in turn, not defined. Firms cannot generate net positive profits, while the banking system’s net worth stays at zero due to zero interest income. Nominal GDP growth and wage and price inflation appear “indeterminate” after a while; they oscillate widely. The experiment confirms the crucial role for interest as a pre-requisite for firm profits and cycles to arise.

Considering a constant base lending rate but forcing realized risk-based spreads to zero lets the cycle amplitude fall significantly (Table 3, Experiment #4, Figure 8). Debt stock-to-GDP flow ratios increase to an extent. The tails of the wage and price inflation distributions become less deep. The Fourier power spectrum estimate falls to less than 0.2, while cyclical behavior remains at a frequency of about 20– 50 periods per cycle. The price and wage Phillips curves are still downward sloping but shifted somewhat. The experiment corroborates that realized risk-based spreads are likely a major source of cycle amplification.

Switching downward nominal wage rigidities off lets cycles disappear and firm profit shares converge to zero (Table 3, Experiment 5, Figure 9). Cycles vanish, full employment is obtained, and hence the wage and price Phillips curves become undefined (vertical). Debt to GDP stabilizes at about 110 percent. No defaults occur. The experiment suggests that downward nominal wage rigidities are among the essential sources for cyclical economic dynamics to arise, and that relaxing them can help reduce structural unemployment. The goods and labor markets in the model are not of a local matching kind, as, for example, in Guerini et al. (2018), where due to that local structure, even in the absence of wage asymmetries a small level of frictional unemployment can arise as a result of market frictions and coordination failures.

Changing the price inflation reference for setting wages from firm-specific toward the economy aggregate lets the cycle frequency increase notably (Table 3, Experiment 7, Figure 10). Experiments #6 and #7 suggest that increasing the weight on aggregate price inflation to determine wage inflation (while maintaining the downward rigidity) lets unemployment rise and the cycle frequency increase. Wage and price Phillips curves become increasingly flat. Firms “embracing” and perfectly measuring economy-wide price inflation to set their own wages therefore removes one source of a slow-moving cyclical dynamic of economic activity, through firms internalizing in every period the sector-aggregate externality of their previous wage decisions. Information rigidities were considered as a result of partial information (Coibion and Gorodnichenko 2015), sticky information (Mankiw and Reis 2002), and noisy information (Woodford 2003, Sims 2003). How variation in those information rigidities influence cyclical behavior at large, as illustrated here, should deserve more examination in future research.

Considering multi-period loans and operating with a conventional, nonlinear amortizing repayment schedule implies for the cyclical model dynamics to not change in any notable way (Table 3, Experiment #8, Figure 11). Any new loan dispersed in Step 2 (Section 3.1) is now granted with a randomly chosen duration, drawing it from a log normal distribution with mean 2 and standard deviation 0.2 and rounding the draws up to the nearest integer. With this calibration, the median and standard deviation of the level duration amount to 7.4 and 1.5, respectively. In case loans are topped up instead of newly granted after a firm is debt-free, the current residual duration just before the top-up and the newly drawn one are combined using a weighted average of the current and top-up loan duration, using the current principal debt outstanding and the top-up principal as weights, and rounding up to the next integer. Conditional on a firm’s current principal outstanding L_f,t-1, a residual duration counter d_f, and the current interest rate i_f,t, the total annuity a_f,t (due in Step 6, Section 3.1) is computed every period as:

\begin{matrix} (8) & a_{f, t} = \frac{L_{f, t - 1} \times i_{f, t} {(1 + i_{f, t})}^{d_{f}}}{{(1 + i_{f, t})}^{d_{f}} - 1} \end{matrix}

The formula nests the case of initial durations equal 1, as in the base model version. The interest payment flow due is $a_{f, t}^{I} = i_{f, t} L_{f, t - 1}$ . The principal repayment flow due is $a_{f, t}^{P} = a_{f, t} - a_{f, t}^{I}$ . The principal balance falls period by period: $L_{f, t} = L_{f, t - 1} - a_{f, t}^{P}$ . This multi-period loan scheme makes hardly any difference for the model dynamics (Figure 11). The cycle frequency and amplitude remain rather unaffected. The unemployment rate distribution has slightly deeper right tails. Otherwise, only the counts of required rollovers and top-up requests fall.

Replacing households’ stochastic firm choice for consumption by a “directed,” constant firm choice lets cycles disappear and a non-stochastic steady state arise (Table 3, Experiment #9). This is the only experiment considered here that results in a deterministic steady state after a short transitory period; Table 3 reports the steady state estimates. All firms remain indebted, never default, do not require any debt top-up, and precisely roll over their principal every period (paying interest only). The experiment confirms that a minimal source of internal stochasticity is instrumental for the cyclical behavior, as described in Section 3.2, to unfold. Importantly, these are small disturbances numerically, and independent of the business cycle state.

Letting households save lets the cycle amplitude rise and its frequency fall (Table 3, Experiment #10). Letting households spend an assumed 75 percent of their stock of savings inclusive of any period’s latest wage income flow (when entering Step 4 in Figure 2) implies for the cycle amplitude to rise and its frequency to fall to an extent. Debt stock-to-GDP flow ratios rise a bit. Nominal and real GDP growth and wage and price inflation dynamics are not affected in any notable way. The experiment suggests that allowing for household saving does not affect the cyclical behavior in a fundamental manner and lets the conclusions from all other experiments still hold up.

4. Discussion

4.1 Minsky and Markups

Minsky (1986)’s chapters 7–9 are central to his financial instability hypothesis, laying out the role of prices, profits, and cash flow commitments. Four observations result from seeing his work in light of the model and its theoretical grounding developed here.

First, he argues that “for a capitalist system to function well, prices must carry profits” (ibid., p. 158). The model here conforms with this statement.

Second, he separates two price systems, for current output and for capital assets, which is distractive to an extent. Capital assets relate to an investment sector that he considers next to consumption goods producers. The model here does not require such a distinction. Paying wages is a form of investment to keep the labor force working instead of its effort depreciating to zero if wage payments were to stop. Likewise, the production of capital investment goods also requires employees to be paid wages. Hence, while it is fine to consider an investment sector in a model, one can save oneself this feature to create space for introducing other elements as long as there is no specific need for the distinction. One can reinterpret Minsky’s two price systems as being about goods prices versus wages more generically and let “capital assets” encapsulate labor. Separating investment and consumption goods producers in the model results in the same dynamic behavior and conclusions as presented in Section 3.

Third, Minsky is not clear as to whether firm market power or debt-financed investment generates firm profits. On one side, he suggests that for a firm to cover its contractual expenses, it requires a markup that it can “control [...] to the extent that it has market power” (ibid., p.159, emphasis added). On the other side, he suggests that debt-financed investment be the source of markups (ibid., p.161, and equations on p.163). Both statements appear misled in view of the model here, which suggests that firm profits at the economy level arise under perfect competition, not requiring market power, in line with a profit-maximizing price setting as in the conceptually identical equation (8) in his book (ibid., p.163) and equation (5) herein. Profits here arise due to a lagged wage-price dependence coupled with debt-financed investment and, crucially, with debt bearing interest (Section 3.3, Experiment #3). The place where his exposition stumbles is on p. 163 (ibid.), eqs. (3)-(6), where he suggests that profits are generated through investment. To see why that is a fallacy: Let an investment goods firm sector income (I) equal its wage bill (WB_I). Thus, its profits, π_I = I-WB_I are 0 by assumption. Let a consumption goods firm sector expense consist of investment (I) and its wage bill (WB_C). Its income equates to consumption (C). Its profits are π_C = C – WB_C -I. Since C = WB_C + WB_I and WB_I = I, the consumption goods firm sector profits are π_C = WB_C + I – WB_C -I = 0. Hence, just introducing a detour of wage flows via investment goods firms cannot generate profits, for neither the components nor the aggregate of the firm sector.¹⁵

Fourth, related, he suggests that an “increasing dominance of markets by firms with market power [...] produces inflationary pressures” (ibid., p. 174, emphasis added). Implied by the previous point, also price inflation here does not arise due to market power but due to the same wage-price process coupled with interest-bearing debt-based investment.

While Minsky lightly addresses the role of interest as part of his taxonomy of cash flows (ibid., p. 223 ff.), he does not integrate interest more fundamentally with the endogenous cycle process.¹⁶ He contemplates that the shares of speculative and Ponzi-financed firms increase throughout boom times, but does not explain why this behavior emerges. The theory developed here attempts to do so. While Ponzi finance dynamics might matter in reality to an extent, they are shown here to not be a requirement for regular debt-driven business cycle behavior to arise, as the model rules that possibility out by design.

Regular debt-driven economic cycles as generated by the model evolve parallel to lower-frequency cycles due to slower-moving structural change (not in-scope of the model). A slower-moving transformation of institutions, conventions, and market structures—jointly referred to as “thwarting institutions” by Ferri and Minsky (1992)—can be seen as a cause for otherwise regular debt-driven recessions to occasionally (at lower frequency) be deeper, in which case they deserve the tag “financial crisis” (Great Depression 1929–33, Global Financial Crisis 2007–09). These entail more significant defaults of financial institutions than regular downturns. One may say that the financial system, banks in particular, “survive” a few regular downturns with leverage not entirely correcting, and only after sufficient structural change has weakened it, it crashes more materially along with a downturn that would have anyways occurred. Slow-moving structural change manifests itself, for example, through the slow tightening and relaxation of bank regulation, or the slowly rising relevance of mortgage debt throughout the 20^th century (Jordà et al. 2016b). Structural change implying lower frequency cycles may square with the empirical finding that financial cycles have longer durations than business cycles (Strohsal et al. 2019). Others conclude, however, that such evidence is not that strong and that the estimates are generally surrounded by notable uncertainty (Cagliarini and Price 2017).

Further related to firm markups, the theory here resembles some rationale of Monetary Circuit Theory (MCT) but goes beyond it. MCT (Graziani 1989, 2003) focuses on monetary flow processes, considering bank lending for firms to cover their wage bill ahead of production; in line with the model structure here. MCT has moved into stalemate, however. Rochon (2005, p.125) notes: “The existence of monetary profits at the macroeconomic (aggregate) level has been a conundrum for theoreticians of the monetary circuit. [...] Not only are firms unable to create profits, they also cannot raise sufficient funds to cover the payment of interest.” Bellofiore et al. (2000, p.410) suggest that in the circuit approach, “firms in the aggregate can only obtain the wage bill they advanced to workers and, as a result, it is impossible for all firms to obtain money profits.” I could not find a persuasive answer to this open question in such papers and their surrounding literature. The model here suggests that the answer lies in banks’ interest income being paid out to private sector agents, through deposit interest and dividend flows, and consumers spending such income beyond their wage income to thereby create positive markups for firms at a system level. The system is kept afloat by debt being rolled over, while charging interest on such quasi-perpetual at-the-leash credit money, which leads to an ever-growing nominal money stock. Here, we connect back to the fuller endogenous cycle narrative laid out in Section 3.2.

How the markup dynamics across firms and firm sectors behave as a function of evolving competition is beyond the scope of the model here. Blanchard (2018, p.18) opines: “How markups move, in response to what, and why, is however nearly terra incognita for macro... we are a long way from having either a clear picture or convincing theories, and this is clearly an area where research is urgently needed.” This statement may have two dimensions: cross-firm and cross-sector, as opposed to macro. From a macro viewpoint, the theory here suggests an insight. The cross-firm and cross-sectoral perspective to markup dynamics is beyond its scope, but addressed in Seppecher et al. (2018), where monetary and real, multisector interdependencies are considered in a model with debt-financed investment and inventory management, as in other macro-financial ABMs cited earlier.

4.2 Amplification of Cycles Upon Their Existence

A perspective on four amplification and dampening mechanisms is shown in Figure 12.

The Collateral Accelerator. It rests on the presence of collateral, or firm net worth generically speaking, whose value is procyclical and amplifies (compresses) lending during booms (recessions). The related literature was cited in Section 2 (Bernanke et al., Kiyotaki and Moore, and so on).

The Mispricing Accelerator. It relates to counter-cyclical lending standards (Asea and Blomberg 1998, Ruckes 2004, Jimenez et al. 2006). High-risk loans are granted during boom periods, when the borrower-risk component of lending rates tends to fall, while borrower risk in fact increases when seeing the economy through an endogenous cycle lens. This mispricing during expansions can be traced, in turn, to two sources. Competition is a first. Stronger competition leads to lower lending rates and higher deposit rates, hence lower net interest income (NII) for banks and thus higher incentives for risk taking (Boyd and De Nicolo 2005). Bank capital ratios tend to fall due to higher competition during booms, due to structural shifts in competition (Keeley 1990) and certainly due to cyclical variation in demand and implied cyclical competition for the supply of loans, too. The margin effect (Martinez and Repullo 2010), whereby loan spreads and banks’ NII fall due to rising competition, dominates in competitive markets. The reason for connecting the Collateral and Mispricing Accelerator in Figure 12 is that some borrower-risk measures, such as a loan-to-value (LTV) ratio, involve the (procyclical) value of collateral, for that metric to have implications for pricing. A second cause of the Mispricing Accelerator relates to the notion that “volatility does not measure risk” (Danielsson et al. 2012/16a/b). Risk measurement in the banking industry involves PDs; Moody’s KMV-like PDs are widely used, for instance (Crosbie and Bohn 2003). They are based on a realized variance rationale (as in equation (2) in the model) and may not measure risk in a sufficiently forward-looking way, in particular nearby a cycle’s turning point when longer duration loans such as mortgages are prone to be underpriced, when low variance dominates high leverage in Merton-type models. This mismeasurement may lead to too low (high) loan prices and insufficient (too sizable) loss provisioning as well as inflated (too low) risk weights during booms (recessions). Competition may imply that this is intentionally overlooked as deviating to a higher loan price, better reflecting actual risk, and would imply for a bank to “price itself out of the market” and face a loss in profit and market share. Another way for banks to misprice longer-term loans may lie in their use of maturity-insensitive pricing models, which a survey of UK banks revealed (Cadamagnani et al. 2015). The presence of competition also may make such model choice intentional.

The Policy Accelerator. A third source of procyclical lending stems from regulatory policy (Blum and Hellwig 1995). Models of optimal bank capital were developed to help see the procyclical effects of regulation (Estrella 2004, Angeloni and Faia 2013). The Basel II framework has been assessed to be more procyclical than Basel I (Kashyap and Stein 2004), as the former is risk-based, while the risk measures may not properly measure actual risk. Countercyclical policy as considered in Basel III regulation is meant to dampen procyclical effects.¹⁷ On the accounting side, the International Financial Reporting Standard 9 (IFRS 9) and the Current Expected Credit Loss (CECL) methodology have been introduced, motivated in large part by their intention to compress procyclical lending.

The Herding Accelerator. Herding behavior in investment can arise despite being socially inefficient (Scharfstein and Stein 1990) and swings of optimism and pessimism can be due to people mimicking the actions of others (Becker 1991, Kirman 1993).¹⁸ The Herding Accelerator operates on top of the Mispricing and Policy Accelerator, insofar as banks tend to herd on the same models (model philosophy generally), leading to mispricing and misprovisioning in a synchronized way for all banks. Regulation is imposed on the banking system and is in that sense a built-in herding mechanism, too. Memory-based bounded rationality (Mullainathan 2002) and, related, the institutional memory hypothesis (Berger and Udell 2004) suggest that economic agents tend to forget the lessons of past recessions and crises, including through new generations replacing older ones. Along a boom period, they forget that the models used for pricing and provisioning underestimate risk, while competition implies little incentive to remember and counteract. It is rational from a micro perspective to herd, which links to the notion of “sharing the blame” (Scharfstein and Stein 1990) and Keynes noting that “worldly wisdom teaches that it is better for reputation to fail conventionally than to succeed unconventionally” (Keynes 1936, p.157).

Additional, structural sources of cycle amplification stem from interconnectedness. These include firm interconnectedness through supply chains (Delli Gatti et al. 2010), bank interconnectedness via interbank reserve lending relationships (Krug et al. 2015, Popoyan et al. 2020), and firm-bank cross-interconnectedness through banks’ lending to the economy. All three forms imply for default cascades arising in some part of the economy to propagate in a more amplified manner than otherwise. A form of indirect firm network connectedness through the demand side has been reflected in the model here. From among the four accelerator types in Figure 12, the realized risk-based mispricing accelerator is embedded in the model (equation 2).

5. Conclusions

The model developed here is of a rather pure monetary cycle kind and can be called a “Dynamic Stochastic General Disequilibrium” (DSGD) model. The “small shocks, large cycles puzzle,” so called in Bernanke et al. (1996), is not a puzzle in this model, but easily explained (Section 3). The list of what the model did not require includes, for example, rational expectations, demand expectation-driven investment, external habit formation regarding consumption, inventory management, Calvo price setting, a distinction between producers and retailers with the latter acting under monopolistic competition to generate price stickiness, and so on. The disequilibrium model instead reflects two assumptions: the presence of interest-bearing debt and a degree of downward wage rigidity, which, respectively, reflect institutional and behavioral reality and serve to micro-found the model.

Unlike suggested by Minsky, it is not debt-financed investment as such that generates firm profits at the macro level, but it is interest that generates profits. The stock-flow consistent model with its system-wide scope reveals this aspect. Principal debt for investment (wages) just flows forth to consumers and back to firms, rendering economy-wide net profits nil. The continual addition of interest-bearing debt and lenders paying some of the interest income to consumers, and them spending it, is a prerequisite for profits to arise dynamically over time.

Despite its simplicity, the model generates endogenous cycles and replicates six stylized facts.

These are summarized in the abstract and introduction of the paper and laid out in detail in Section 3.

The meaning of “stochastic” (S) in DSGD is different from what it is in DSGE. In DSGE models, shocks are sizable and required to generate half-cycles back to steady state. In the DSGD model here, shocks are of a small, unnoticeable kind (demand perturbations, small endogenous base rate or credit spread moves), which nearby a turning point cause downturns before another upturn emerges endogenously.

A literature perspective was meant: (1) to relate to system dynamics models, concluding that they are not well suited for allowing for explicit agent default as they built on a representative agent structure just as much of the DSGE model stream, and that their dynamic behavior is sensitive to functional assumptions and parameters; (2) to note that ABMs are amenable to stock-flow consistent dynamic modeling, allowing for agent defaults (which is key for achieving the aim of generating cycles), while they have become very comprehensive, not yet focused on the fundamental drivers of endogenous cycles, and not yet generating cycles of a so regular kind as illustrated here; and (3) to reflect on sources of amplification and dampening of cycles upon their existence, which led to the suggested categorization of four accelerator types: collateral, mispricing, policy, and herding, next to structural sources of amplification stemming from network interconnectedness. The mispricing accelerator and a demand-side feedback from firm defaults are reflected in the model.

Robert Lucas suggested that good models shall necessarily be “abstract” and “patently unreal” (Lucas 1980, p. 697), with which I strongly disagree. The model here, just as numerous emerging macro-financial ABMs, is not abstract and meant to be reflective of institutional and behavioral reality, disciplined by the stock-flow consistency principle as prevalent in Post-Keynesian economics, and with a system-wide perspective. For the latter reason, “general” (G) is suggested to be included in DSGD. It is in line with Stiglitz’s perspective that theories are valuable if reflective of “how firms and households actually behave and markets actually work” (Stiglitz 2017, p. 4). As a next step, the bare bones model structure can be extended to examine the fundamental channels for monetary, fiscal, and macroprudential policies to influence cycle dynamics, and the model subsequently be estimated on empirical data.

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Contributor Notes

Abstract

1. Introduction

2. Literature

2.1 Equilibrium and Disequilibrium Theory

2.2 Downward Nominal Wage Rigidities

2.3 Macro-Financial ABMs

3. Model and Simulations

3.1 The Model

3.2 Base Simulation and Economic Cycle Narrative

3.3 Structural Experiments

4. Discussion

4.1 Minsky and Markups

4.2 Amplification of Cycles Upon Their Existence

5. Conclusions

References