Does slow growth lead to rising inequality? Some theoretical reflections and numerical simulations


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Ecological Economics


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Ecological Economics xxx (2015) xxxxxx






Does slow growth lead to rising inequality? Some theoretical reflections and numerical simulations

Tim Jackson a,, Peter A. Victor b

a Centre for Environmental Strategy, University of Surrey, Surrey, UK

b Faculty of Environmental Studies, York University, 4700 Keele Street, Toronto, Canada




a r t i c l e          i n f o  


Article history:

Received 4 August 2014

Received in revised form 10 February 2015 Accepted 16 March 2015

Available online xxxx


Keywords: Social justice Inequality


Stock flow consistent modelling Savings



a b s t r a c t  


This paper explores the hypothesis (most notably made by French economist Thomas Piketty) that slow growth rates lead to rising inequality. If true, this hypothesis would pose serious challenges to achieving prosperity with- out growth or meeting the ambitions of those who call for an intentional slowing down of growth on ecological grounds. It would also create problems of social justice in the context of a secular stagnation. The paper describes a closed, demand-driven, stock-flow consistent model of Savings, Inequality and Growth in a Macroeconomic

framework (SIGMA) with exogenous growth and savings rates. SIGMA is used to examine the evolution of in- equality in the context of declining economic growth. Contrary to the general hypothesis, we find that inequality does not necessarily increase as growth slows down. In fact, there are certain conditions under which inequality can be reduced significantly, or even eliminated entirely, as growth declines. The paper discusses the implications of this finding for questions of employment, government fiscal policy and the politics of de-growth.

© 2015 Elsevier B.V. All rights reserved.








1. Introduction


The French economist, Piketty (2014a), has received widespread ac- claim for his book Capital in the 21st Century. Building on over 700 pages of painstaking statistical analysis, the central thesis of the book is none- theless relatively straightforward to describe. Piketty argues that the in- crease in inequality witnessed in recent decades is a direct result of the slowing down of economic growth in modern capitalist economies. Under circumstances in which growth rates decline further, he suggests, this challenge would be exacerbated.

So, for example, any future movement towards a ‘secular stagnation’

(Gordon, 2012; MGI, 2015; OECD, 2014) is likely to be associated with even greater inequality. Equally, any policies aimed at deliberately ‘dethroning’ the Gross Domestic Product (GDP) as an indicator of prog-

ress (Turner, 2008) could have perverse impacts on the distribution of incomes. Likewise, any objective of ‘degrowth’ for ecological or social reasons (Kallis et al., 2012; Latouche, 2007; Schneider et al., 2010) might be expected to have undesirable social outcomes.

Piketty's hypothesis that a slowing down of growth increases structural inequality poses a particular challenge to those ecological



Meadows et al., 1972), have been critical of society's ‘GDP fetish’ (Stiglitz et al., 2009) and sought to establish alternative approaches (d'Alisa et al., 2014; Daly, 1996; Jackson, 2009; Rezai et al., 2013; Victor, 2008) in which socio-economic goals are achieved without assuming continual throughput growth.1 Certainly, the prospects for ‘prosperity without growth’ (Jackson, 2009) would appear slim at best if Piketty's thesis were unconditionally true.

The aim of this paper is therefore to unravel the extent of this challenge in more detail. To this end, we develop a simple closed, demand-driven model of Savings, Investment and Growth in a Macro- economic framework (SIGMA).2 We then use SIGMA to test for the implications of a slowdown of growth on a) capital's share of income and b) the distribution of incomes in the economy. By adding a govern- ment sector to the model, we are able to explore the potential to miti- gate regressive impacts through a progressive taxation system. The inclusion of a banking sector allows us to establish clear relationships between the real and the financial economy and discuss questions of household wealth. Our ultimate aim is to tease out the implications

of our findings for the wider project of developing an ‘ecological


economists who, from the earliest days of the discipline (Daly, 1972;                                      

1 For an overview of such alternative approaches see pke, this volume.

2  A user-version of the SIGMA model is available online at http://www.prosperitas.


* Corresponding author.

E-mail address: (T. Jackson).


org,uk/sigma to allow the interested reader to reproduce the results in this paper and con- duct their own scenarios.

0921-8009/© 2015 Elsevier B.V. All rights reserved.




macroeconomics’. First, however, we outline the structure of Piketty's argument in more detail.


law, Eq. (3) suggests that over the long term, capital's share of income is governed by the following relationship:




2. Piketty's Two ‘Fundamental Laws’ of Capitalism


There are two core strands to Piketty's case. One of them (Piketty,



α→r g ast:




2014a: 22–25) concerns the power that accrues increasingly to the owners of capital, once the distribution of both capital and income becomes skewed. The power of accumulated or inherited wealth to set the conditions for the rates of return to capital and labour increasing- ly favours the owners of capital over wage-earners and reinforces the advantages of the rich over the poor. These arguments are of course relatively well-known from Marxist and post-Marxist critiques of capitalism (Buchanan, 1982; Goodwin, 1967; Giddens, 1995).

Piketty's principal contribution, however, is to identify what he calls a ‘fundamental force for divergence’ of incomes, in the structure of mod- ern capitalism (Piketty 2014a: 25–27). In the simplest possible terms it

relates to the relative size of the rate of return on capital r to the growth rate g. When the rate of return on capital r is consistently higher than the rate of growth g, it leads to an accumulation of capital by the owners of capital and this tends to reinforce inequality, through the mechanism described above.

Piketty advances his argument through the formulation of two ‘fundamental laws’ of capitalism. The first of these (Piketty, 2014a: 52 et seq) relates the capital stock (more precisely the capital to income ratio β) to the share of income α flowing to the owners of capital. Specifically, the first fundamental law of capitalism says that3:


α ¼ rβ;                                                                                                            ð1Þ


where r is the rate of return on capital. Since β is defined as K/Y where K is capital and Y is income, it is easy to see that this ‘law’ is, as Piketty ac- knowledges, an accounting identity:


αY ¼ rK:                                                                                                          ð2Þ


Formally speaking, the income accruing to capital equals the total capital multiplied by the rate of return on that capital. Though this ‘law’ on its own does not force the economy in one direction or another, it provides the foundation from which to explore the evolution of historical relationships between capital, income and rates of return. In

particular, it can be seen from this identity that for any given rate of return r the share of income accruing to the owners of capital rises as the capital to income ratio rises.4

It is the second of Piketty's ‘fundamental laws of capitalism’ (Piketty

2014a: 168 et seq; see also Piketty, 2010) that generates particular con- cern in the context of declining growth rates. This law states that in the long run, the capital to income ratio β tends towards the ratio of the sav- ings rate s to the growth rate g, i.e.:



β→ g ast:                                                                                                  ð3Þ


This asymptotic law suggests that, as growth rates fall towards zero, the capital to income ratio will tend to rise dramatically — depending of course on what happens to savings rates. Taken together with the first




3 In what follows, we suppress specific reference to time-dependency of variables ex- cept where absolutely necessary. Thus all variables should be read as time dependent un- less specifically denominated with a subscripted suffix 0. Occasionally, we will have reason to use the subscripted suffix (1) to denote the first lag of a time-dependent variable.


In other words, as growth declines, the rising capital to income ratio β leads to an increasing share of income going to capital and a declining share of income going to labour. Unless the distribution of capital is itself entirely equal (a situation we discuss in more detail later) this relation- ship therefore presents the spectre of a rapidly escalating level of income inequality. Rising wealth inequality would also flow from this.

Differential savings rates – in which higher income earners save propor-

tionately more than lower income earners (or, equally, where there are lower propensities to consume from capital than from income) – would reinforce these inequalities further by allowing the owners of capital to

accumulate even more capital and command even higher wages. The superior power of capital (Piketty 2014a 22–25) then precipitates a ris- ing structural inequality.

It is important to stress that relationships (3) and (4) are long-term equilibria to which the economy evolves, provided that the savings rate s and the growth rate g stay constant. As Piketty points out, ‘the accumu- lation of wealth takes time: it will take several decades for the law β =

s/g to become true’ (Piketty 2014a: 168). In any real economy, the

growth rate g and the savings rate s are likely to be changing continual- ly, so that at any point in time, the economy is striving towards, but may never in fact achieve, the asymptotic result. Nonetheless, as Krusell and

Smith (2014: 2) argue, Eq. (4) is ‘alarming because it suggests that, were

the economy's growth rate to decline towards zero, as Piketty argues it will, capital's share of income could increase explosively’.

The principal aim of this paper is to test this hypothesis; i.e. to deter- mine the extent to which declining rates of growth in national income, NI, might lead to rising capital to income ratios and thence to an increas- ing share of income to capital. In either formulation, much depends on the parallel movements in the rate of return on capital r and on the savings rate s. In order to explore these relationships in more detail, we built a simple macroeconomic model of savings, inequality and growth, calibrated loosely against UK and Canadian data. The back- ground and structure for the model are described in the next section. The subsequent section presents our findings.


3. The SIGMA Model


Working together over the last four years, the authors of this paper have developed an approach to macroeconomics which seeks to inte- grate ecological, real and financial variables in a single system dynamics framework (Jackson et al., 2014; Jackson and Victor, 2015).

An important intellectual foundation for our work comes from the insights of post-Keynesian economics, and in particular from an ap- proach known as Stock-Flow Consistent (SFC) macro-economics, pioneered by Copeland (1949) and developed extensively by Godley and Lavoie (2007) amongst others.5 The essence of SFC modelling is consistency in accounting for all monetary flows. Each sector's expendi- ture is another sector's income. Each sector's financial asset is another's liability. Changes in stocks of financial assets are consistently related to flows within and between economic sectors. These simple understand- ings lead to a set of accounting principles which can be used to test the consistency of economic models. The approach has come to the fore in the wake of the financial crisis, precisely because of these consistent ac- counting principles and the transparency they bring to an understand- ing not just of conventional macroeconomic aggregates like the GDP but also of the underlying balance sheets. It has even been argued that


We will see later that the ceteris paribus clause relating to constant r here is important.                                


In fact, the rate of return will typically change as the capital to income ratio rises; and to the extent that this ratio declines with increasing β, it can potentially mitigate the accumu- lation of the capital share of income.


5 Similar post-Keynesian approaches have also been developed by Taylor et al. (2015) and Fontana and Sawyer (this volume). A paper by Campiglio (2015) explores policy im- plications drawn from such approaches.




Fig. 1. High-level structure of the SIGMA model.



the financial crisis arose, precisely because conventional economic models failed to take these principles into account (Bezemer, 2010). Certainly, Godley (1999) was one of the few economists who predicted the crisis before it happened.

For the purposes of this paper, we have employed a simplified ver- sion of our overall approach. SIGMA is a closed, stock-flow consistent, demand-driven model of savings, inequality and growth in a macroeco- nomic framework. The model has four financial sectors: households, government, firms and banks (Fig. 1). Firms' and banks' accounts are di- vided between current and capital accounts and the households sector is further subdivided into two subsectors (which we denominate as

‘workers’ and ‘capitalists’) in order to explore potential inequalities in

the distribution of incomes and of wealth. The model itself is built



Table 1

Financial balance sheet for the SIGMA economy.


using the system dynamics software STELLA. This kind of software provides a useful platform for exploring economic systems for several reasons, not the least of which is the ease of undertaking collaborative, interactive work in a visual (iconographic) environment. Further ad- vantages are the transparency with which one can model fully dynamic relationships and mirror the stock-flow consistency that underlies our approach to macroeconomic modelling.

Following much of the SFC literature, the model is broadly Keynesian in the sense that it is demand-driven. Our approach is to establish a level of overall demand through an exogenous growth rate, g, and to generate the level of investment through an exogenous savings rate, s. We then explore the impacts of changes in these variables over time on the income shares from capital and labour through an endogenous rate of return, r, on capital. To achieve this we employ a constant elasticity of substitution (CES) production function, not to drive output as in a con- ventional neoclassical model, but to derive the marginal productivity rK


                                                                                                                                       of capital K and also to establish the labour employment associated with


                                     Households          Firms           Banks        Govt       Total           


a given level of aggregate demand.6

To illustrate our arguments without unnecessary complications, we work with a simplified version of the more complex structure that we have developed elsewhere (Jackson and Victor, 2015). First, as noted, the SIGMA economy is closed with respect to overseas trade. Next, we




Net financial assets Financial assets

D + E D + E




–            0

–            D + E + L





–            D




–            L





–            E

Financial liabilities

L + E


–            L + E + D




–            D




–            L




–            E




We are aware of course of the limitations of using a broadly neoclassical production function (Cohen and Harcourt, 2003; Robinson, 1953). However, retaining this aspect of


                                                                                                                                       Piketty's analysis allows us to compare our findings more directly with his.




assume that government always balances the fiscal budget and holds no outstanding debt, so that government spending, G, is equal to taxes, T,

levied only on households. Finally, we employ a rather simple balance


Noting that we can substitute T = Tw + Tc for G and Cw + Cc for C on the right hand side of Eq. (13), and rearranging terms, we find that:


sheet structure (Table 1), sufficient only to get a handle on changes in


Inet¼  Yh C  T


þ Yh C T



þ  P fr if




household wealth under different patterns of ownership of capital.


w              w               w)


c              c             c )                       :


Households assets are held either as deposits, D, in banks or as equities,

E, in firms. The only other category of assets/liabilities are the loans, L,


The first two terms in parentheses on the right side are, respectively, the savings Sw of workers and the savings Sc of capitalists, and the third


made by banks to non-financial firms. The banking sector plays a rela-                                            h                                                                                                        h












tively straightforward role as a financial intermediary, providing deposit facilities for households and loans to firms. Clearly none of these



term represents the savings Sf of nonfinancial firms. Accordingly, we can rewrite Eq. (14) as:


assumptions is accurate as a full description of a modern capitalist economy, but all of them can be relaxed in more sophisticated versions


Inet ¼ Sh


þ Sh


þ Sf S;                                                                                  ð15Þ


of our framework and none of them obstructs our purposes in this paper. We follow Piketty in focussing our primary attention on the net national income, NI, which can be defined both as the total income in

the economy:


NI ¼ W þ P þ i                                                                                               ð5Þ


where W represents wages, P profits (including rents), and i net interest receipts, and also as the demand by households, firms and government for goods, services and (net) investment in fixed capital:


NI ¼ C þ G þ Inet ;                                                                                            ð6Þ


where C is consumer spending, G is government spending and Inet is net investment. The gross domestic product is then given by:


where S is the total savings across the economy. Eq. (15) is a special form of the so-called ‘fundamental accounting identity’ (Dorman, 2014: 86) for a closed economy with a balanced fiscal budget. In SIGMA, the overall evolution of savings is determined by an exogenous

savings rate, s, with respect to the national income, so that net savings across the economy are given by:


S ¼ sNI:                                                                                                         ð16Þ


For the purposes of the exploration in this paper, we assume that s takes a fixed value s0 throughout each scenario. Since we are interested in the impact that different savings rates might have on different types of households, however, we allow the savings rate, sw, of workers to be varied exogenously in different scenarios, so that the savings of worker households are given by:


GDP ¼ NI þ δ0 K ¼ C þ G þ I;                                                                       ð7Þ          Sw


w              w)



where K is the value of the capital stock, δ0 is a (fixed) depreciation rate


h  ¼ sw  Yh T


:                                                                                       ð17Þ


and gross investment I is given by:


I ¼ Inet  þ δ0 K:                                                                                                 ð8Þ


In order to ensure that overall savings satisfy Eq. (16), the savings of

capitalists are then determined as a balancing item.


Sc                              w



Since the two methods of calculation in Eqs. (5) and (6) both lead to an equivalent net national income, it follows that:


W þ P þ i ¼ C þ G þ Inet :                                                                                 ð9Þ


Profits P are generated both by nonfinancial firms and by banks. Banks' profits Pb are simply the difference between the interest, if = rlL1, charged to firms on loans and the interest, ih = rdD1, paid to households on deposits. We assume that banks distribute all of these profits to households. Nonfinancial firms on the other hand retain an

exogenously determined proportion rf of their total profits. Retained profits Pfr are then equal to rfPf and the remainder, Pfd = Pf Pfr are dis-

tributed to households. Eq. (9) can therefore be rewritten as:


W þ Pb þ P fd þ P fr þ ih if  ¼ C þ G þ Inet :                                                     ð10Þ


h  ¼ SSh Sf :                                                                                             ð18Þ


Household savings are distributed between new bank deposits, ΔD, and the purchase of equities, ΔE, from firms. It is assumed for simplicity that the demand for new equities by households is equal to the supply of new equities by firms and that these in their turn are determined via a desired debt to equity ratio in firms.7 The distribution of equity purchases between capitalist and worker households is deemed to be in the same proportion as the net savings of each sector. Changes in deposits are then calculated as a residual from net savings.

In order to model the evolution of the SIGMA economy over time, we follow Piketty by defining the evolution of the net national income NI according to an (exogenous) growth rate g such that:


NI ¼ ð1 þ gÞ * NIð1Þ                                                                                                                                                                           ð19Þ


where NI(1) is the value in the previous period (i.e. the first lag) of the

fixed value g0 throughout the


Since Pb = if ih, we can also write Eq. (9) as:


W þ P fd þ P fr  ¼ C þ G þ Inet ;                                                                       ð11Þ






and it becomes clear that in the SIGMA model at least, bank profits do not contribute to the national income which consists only in wages and firms' profits. Furthermore, if we define the household income, Yj , for each household type j according to:



Y j                      j                j                 j                  j


variable NI. In some scenarios g will take a

period τ of the scenario,8 whilst in others g will decline uniformly from

g0 to zero over time t.

Testing Piketty's hypothesis requires that we establish the rate of re- turn to capital, r, which in turn allows us to determine the split between wages and firms' profits in the net national income. Along with Piketty

(2014a: 213–214), we assume (for now) that the return to capital is

given by the marginal productivity of capital, which we denote by rK. This assumption only works under market conditions in which there

are no structural features which might lead either capital or labour to


h ¼ W


þ Pb þ P fd þ ih ;                                                                              ð12Þ


tort more than their ‘fair’ share of the output from production. In a


with j ∈ {w, c}, where w represents workers and c represents capitalists, then, Eq. (10) can be rewritten as:


Yw                  c

h  þ Yh þ P fr if  ¼ C þ G þ Inet :                                                                     ð13Þ




In contrast to our treatment elsewhere (Jackson and Victor, 2015), this means that there is no speculative purchasing of equities that might lead to capital gains and losses.

8  In this paper we take τ = 100, i.e. the scenarios run over 100 years.



Table 2

Transactions ow matrix for the SIGMA economy.






















Consumption (C)











Gov spending (G)











Investment (I)











Wages (W)











Profits (P)

w             w

+ Pfd + Pb

c              c

+ Pfd + Pb



+ Pfr






Taxes (T)











Interest                                        + rdDw                                           + r Dc                                             r L                                                + r L    r D                                                                      0

1                                                  1                                                   l  1                                                                                                 l  1                1

Change in deposits (D)








+ ΔD



Change in loans (L)





+ ΔL






Change in equities (E)





+ ΔE



















sense, this assumption is a conservative one for us, to the extent that conclusions about inequality are stronger in imperfect market dynamics. Under conditions of duress, in which the owners of capital receive a rate of return r greater than the marginal productivity of capital rK, our conclu- sions about any inequality which results from declining growth rates will be reinforced. Conversely, of course, we must be aware of making too strong assumptions about the potential to mitigate inequality, in any situation in which the owners of capital have greater bargaining power than wage labour.

With these caveats in mind, the next step is to determine the marginal productivity of the capital stock. In SIGMA, we achieve this through the partial differentiation of a constant elasticity of substitution (CES) production function of the form first developed by Arrow et al. (1961) in which output, Y, is given by:



It may be observed from Eq. (23), as Piketty also points out (2014b: 37–39), that for σ N 1, (and assuming that the capital to income ratio is greater than one) capital's share of income is an increasing function of the capital to income ratio. As the capital to income ratio rises, capital's share of income increases. Conversely however, when 0 b σ b 1, then

capital's share of income is a decreasing function of the capital to income ratio. As the share of capital to income rises, capital's share of income decreases. At σ = 1, the decline in the rate of return to capital always exactly offsets the rise in the capital to income ratio, and the share of income to capital remains constant. We explore the implications of these findings in the following section.

Armed with Eq. (23), we are now able to derive the profits of firms



P f  ¼ rK K ¼  αNI;                                                                                          ð24Þ


(  ðσ







ðσ1Þ      ðσ




σ                                                         σ



YðK; L; σÞ ¼  aK



þ ð1aÞðALÞ


;                                           ð20Þ


and calculate the income of worker and capitalist households from Eq. (12). Taxes are determined by exogenous tax rates on household


where σ is the elasticity of substitution between labour and capital, a (as described by Arrow et al. (1961) is a ‘distribution parameter’ and A is the coefficient of technology-augmented labour, which we will assume changes over time according to the rate of growth of labour productivity in the economy.9 With a little effort, it can be shown via partial differen- tiation of Eq. (20) with respect to K that the marginal productivity of

capital rK is given by:


income (and in some scenarios on household wealth), savings are determined through Eqs. (16)–(18) and consumption can then be derived as a residual:


C j ¼ Y j T j Sj:                                                                                              ð25Þ




Eqs. (10) through (25) allow for a full stock-flow consistent specifi-


r        Y      aβ

K  ¼ K ¼











cation of the SIGMA economy. Table 2 summarises the flows within and between sectors in a single ‘transactions flow matrix’ (Godley and Lavoie, 2007: 39). It is to be noted that all row totals and column totals in Table 2 sum to zero, reflecting principles of stock-flow consistency


where β is the capital to income ratio.10 Th relationship can now be used to derive the return to capital rKK through:



rk K ¼ aβ σ  K:                                                                                                ð22Þ


Taking the net national income NI as Y, and using Piketty's first law of capitalism (Eq. (2)) it follows that capital's share of income α is given by:


 σ 1

α ¼ aβ σ   :                                                                                                     ð23Þ



9 It can be shown that, for the special case σ = 1, this CES function reduces to the famil- iar CobbDouglas production function Y = Ka(AL)1 a. The introduction of an explicit elasticity variable allows for a more flexible exploration of the production relationship un- der a variety of different assumptions about the elasticity of substitution between labour and capital.

10 Note that as σ → 1, this relationship returns to the first law of capitalism (Eq. (1)) with a = α. In other words, under an assumption of unit elasticity of substitution between capital and labour (as in the Cobb Douglas function), the constant a is given by the share of income to capital α.


that each sector's expenditure is another sector's income (row totals) and that the sum of incomes and expenditures (including savings) in each sector must ultimately balance. It is also pertinent to observe that

one of these sector balances has been left unspecified in Eqs. (10)–(25):

namely, the equation that balances banks' capital accounts:


ΔL ¼ ΔD:                                                                                                      ð26Þ


Although ΔL was defined via firms financing requirements and ΔD was defined as the residual from household savings, the balance Eq. (26) is not in itself imposed as a constraint on the model. Rather, it should emerge as a result of all the other transactions in the economy, provided that the model itself is indeed stock-flow consistent (cf

Godley and Lavoie, 2007: 67–8). Eq. (26) is therefore a useful check

on the validity of the model as a whole. Since loans are created in the model as a financing demand, and deposits are a residual from house- hold incomes, once all other outgoings are accounted for, we could also regard Eq. (26) as an illustration of the post-Keynesian claim that

‘loans create deposits’ (BoE, 2014), in contradistinction to the claim of

conventional monetary economics that ‘deposits create loans’. Indeed, it  is  possible  to  test  this  claim  further  by  reducing  the  new  loan




requirements of firms (for instance by increasing the retained profit ratio) and observing that the level of new deposits in the economy does indeed decline.

In order to reflect the levels of inequality in different scenarios, we introduce a simple index of income inequality qy defined by:

(Yc                    \


than that of workers. It can of course be considerably higher than 100 and we shall see this in some of the scenarios described in the following section.

For the purposes of exploring Piketty's hypothesis that declining growth rates lead to rising inequality, the model described in this section is now complete. However, we note here that the production

function in Eq. (20) can also be used to derive the labour requirements


qY  ¼


dh 1














* 100                                                                                ð27Þ


in the SIGMA economy, according to:


c                           w                                                                                                                                                                                                                             1 ( 1




 σ 1




 σ 1











where Ydh and Ydh represent the disposable incomes of capitalists and

workers (respectively). Note that in contrast to a more conventional index of inequality such as the Gini coefficient or the Atkinson index







At     1a



:(Y σ   aK σ


:                                                           ð28Þ


(Stymne and Jackson, 2000; Howarth and Kennedy, this volume) our inequality index is unbounded. This choice allows us to illustrate nu- merically and graphically the divergence (or convergence) of incomes as growth declines. The index takes a value of 0 when the incomes of capitalists and workers are identical, i.e. there is no inequality at all, and a value of 100 when the income of capitalists is 100% higher (say)


Since the pressure on unemployment is another of the threats from slower or zero growth, Eq. (28) will turn out to be a useful addition to the SIGMA model.

Our principal aim in this paper is conceptual. We aim to unravel the dynamics which threaten to lead to inequality under conditions of de- clining growth. SIGMA is therefore not inherently data-driven. Rather




Fig. 2. a: Long-term convergence of the capital to income ratio with s and g held constant. b: Long-term convergence of capital's share of income with s and g held constant.




Fig. 3. a: Long-term behaviour of the capital to income ratio as g goes to zero (σ = 1). b: Long-term behaviour of capital's share of income as g goes to zero (σ = 1).



it aims to model the system dynamics that connect savings, growth, investment, returns to capital and inequality. It is nonetheless useful to ground the initial values of our variables in numbers which are reasonable or typical within modern capitalist economies. Of particular importance, are reasonable choices for the initial values of the capital to income ratio, the savings rate and capital's share of income. Appendix 1 sets out the representative values chosen for the SIGMA variables, informed by empirical data for recent years.11


4. Results


In  the  first  instance,  it  is  useful  to  illustrate  the  extent  to  which Piketty's ‘laws of capitalism’ hold true. Fig. 2a shows the capital to


11 Data for the Canadian economy may be found in the Cansim online database: http://; and for the UK economy on the Of- fice for National Statistics online database: html?nscl=Economy#tab-data-tables.


income ratio (β) and the ratio (s/g) of savings rate to growth rate, when both s and g are held constant, for the values chosen in our reference sce- nario. Fig. 2b shows capital's share of income (α) alongside the ratio rs/g, under the same conditions. For these conditions, it is clear both that the convergence predicted by Piketty occurs, although it is also clear that this convergence takes some time (around a century in this case).

It is worth remarking that the capital to income ratio β clearly con- verges towards the ratio s/g (Fig. 2a). However, Fig. 2b seems to suggest that, rather than α converging towards the ratio rs/g, the ratio rs/g converges towards α. This is because of a particular feature of our initial values, the choice σ = 1. In these circumstances, as we noted above, the rate of return on capital (calculated as the marginal productivity of cap- ital) moves in such a way as to exactly offset the increase in the capital to income ratio and keep capital's share of income constant. Interesting- ly, this remains the case whatever happens to the growth rate. So for instance, in Fig. 3, we allow the growth rate g to decline to zero. The ratio s/g therefore goes to infinity over the course of the run. As expect- ed, the capital to income ratio β rises substantially (Fig. 3a) more than




Fig. 4. Long-term behaviour of capital's share of income as σ varies (g → 0).





doubling to reach around 9 by the end of the run. It is comforting to note, however, that it does not explode uncontrollably, in spite of Piketty's second law. Even more striking is that capital's share of income α once again remains constant (Fig. 3b), because the rate of return r falls exactly fast enough to offset the rise in the capital to income ratio.

Notice that this lack of convergence of α towards rs/g is not a refuta- tion of Piketty's law, since g is not held constant over the run. This result does go some way, however, to mitigate fears of an explosive increase in inequality as growth rates decline. Indeed, as Fig. 3b makes clear, if the elasticity of substitution σ is exactly one, then the decline of the growth rate to zero has no impact at all on capital's share of income.12

The stability of capital's share of income only holds, however, when the elasticity of substitution between labour and capital is exactly equal to one. Fig. 4 illustrates the outcome of the same scenario (g → 0) on capital's share of income for three different values of σ: 0.5, 1 and 5, chosen to reflect the range of values found in the literature (Appendix 1). As predicted, when the elasticity of substitution σ rises above one, capital's share of income increases. Indeed, when σ equals 5, capital's share approaches 75% of the total income. Piketty notes (2014b: 39) that the (less dramatic) increases in capital's share of income visible in the data over the last decades are consistent with an elasticity in the region of 1.3 to 1.6.

Conversely, however, with an elasticity of substitution less than 1, capital's share of income declines over the period of the run, in spite of the fact that both s/g and rs/g go to infinity. This is an important finding from the point of view of our aim in this paper. To re-iterate, there is no necessarily inverse relationship between the decline in growth and the share of income to capital. Rather, the impact of declining growth on capital's share of income depends crucially on the rate of return on capital which depends in turn on technological and institutional structure. Spe- cifically, with an elasticity of substitution between labour and capital less  than  one,  and  capital  remunerated  according  to  its  marginal




12 This result (the constancy of capital's share of income) holds irrespective of the as- sumed behaviour of the savings rate s. Note however that there is a wide range of possible variations on the capital to income ratio, when the savings rate is allowed to vary. For in- stance, if the savings rate goes to zero along with the growth rate, then the ratio s/g is con- stant over the run. The capital to income ratio rises very slightly (to around 4.7 by the end of the run) but as before capital's share of income remains constant.



productivity, declining growth can perfectly well be associated with an in- crease in the share of income going to labour.

This theoretical result is not particularly insightful without an ade- quate account of the relationship between capital's share of income and the distribution of ownership of capital assets. Under the conditions of our reference case, both income and wealth are equally distributed between workers and capitalists. For all of the scenarios so far elucidat-

ed, the inequality index therefore remains unchanged — and equal to

zero. There is no inequality in such a society, whatever happens to the share of income going to capital.

Clearly of course, this is not very realistic as a depiction of capitalist society. One of the things we know for sure, not least from Piketty's work, is that the distribution of both wealth and wages is already skewed in modern societies, sometimes quite excessively. One element in that dynamic is the savings rate σ. It is well-documented that the propensity to save is higher in high income groups than in low income groups. Kalecki (1939) proposed that the propensity to save amongst workers was zero and for the lowest income groups in the UK, the data support this view (ONS, 2014).

For illustrative purposes, we suppose next that – for whatever

reason – the savings rate amongst workers is lower than the national

average, at 5% of disposable income. The savings rate of capitalists rises (Eq. (18)) to ensure that the overall savings rate across the econo- my remains at 10%. Fig. 5 shows that this apparently trivial innovation has the immediate effect of introducing income inequality, without any decline in the growth rate and with an entirely equal initial distribu- tion of ownership. In Fig. 5a, incomes amongst capitalists are up to 70% higher than those amongst workers by the end of the period. This is a fascinating corroboration of the in-built structural dynamics through which capitalism leads to the divergence of incomes (Kalecki, 1939; Kaldor, 1955; Wolff and Zacharias, 2007).

Under conditions of slowing growth (Fig. 5b), an interesting phenomenon emerges. For high σ, the inequality between capitalists and workers is exacerbated. When σ = 5, capitalist incomes are over 125% higher than worker incomes by the end of the scenario. By contrast, this situation is significantly ameliorated for low σ. Capitalist incomes are barely 40% above worker incomes at the end of the run when σ is equal to 0.5.

The increases in inequality shown in Fig. 5a and b are stimulated simply by changing the savings rate, assuming a completely equal




Fig. 5. a: Inequality in incomes under differential savings rate (g = 2%). b: Inequality in incomes under differential savings rate (g → 0).




distribution of income and capital at the outset. Fig. 6 illustrates the outcome, once we incorporate inequality in the initial distribution of assets. For the purposes of this illustration, we assume that capitalists

comprise only 20% of the population but own 80% of the wealth — a

proportion that seems relatively conservative from the perspective of today's global distribution (Saez and Zucman, 2014; ONS, 2014; Oxfam, 2015).

For the scenarios in Fig. 6, we also assume (again rather conserva- tively) that the distribution of wages remains equal between the two groups, despite the skewed distribution in asset ownership: capitalists earn 20% of the wages and workers earn 80%. Capitalist incomes are nonetheless immediately around 200% higher than workers because of their additional income from returns to capital. What happens subse- quently depends crucially on the value of σ. With high σ, inequality rises steeply as capitalists protect returns to capital by substituting away from expensive labour. So for instance, when σ equals 5 (scenario


1 in Fig. 6), capitalist incomes are almost 750% higher than worker in- comes by the end of the run. With low values of σ, however, it is possible to reverse the initial inequality, bringing the income differential down until, for σ equal to 0.5 (scenario 3), capitalist incomes are only around 70% higher than worker incomes.

In all the simulations described so far, the retained profits of firms are assumed to be zero. Fig. 6 shows two additional scenarios (1a and 3a), in which this default assumption is relaxed, and firms are deemed to retain 10% of their profits to finance net investment. The impact of this assump- tion on inequality is significant, particularly for high values of σ, where capitalist incomes are reduced from 750% to around 400% of worker in- comes. The impact is lower for low values of σ. Essentially, increasing the retained profits of firms has three related impacts on household fi- nances. Firstly, it reduces the return to capital by lowering the distributed profits from firms. Secondly, it reduces the financing requirement of firms, who consequently issue less new equity and require less debt.




Fig. 6. Income inequality with skewed initial ownership and differential savings.




Less debt for firms also means fewer deposits for households (Eq. (26)). Taken together with the lower requirement for equity this leads to a lower net worth for households. Given differential savings rate and an un- equal distribution of assets, the impact of these changes is greater on cap- italist households than on worker households.

Finally, we explore the possibilities of addressing rising inequality through progressive taxation. It is clear immediately that this task will be much easier when the underlying structural inequality rises less steeply than when it escalates according to the σ = 5 scenario in Fig. 6. In fact, as Fig. 7a illustrates, a modest tax differential (a tax band of 40% applied to earnings higher than the income of workers) and a minimal wealth tax (of only 1.25% in this example) when taken togeth- er could equalise incomes relatively easily when σ = 0.5 but fail to curb the rising inequality when σ = 5.

Fig. 7b shows the per capita disposable incomes of the two segments for the low elasticity case. It is notable that towards the end of the run, capitalist incomes and worker incomes are at the same level even though the overall growth rate has declined to zero, exactly counter to the fear of rampant inequality from declining growth rates which motivated this study. Indeed, extension of the model run beyond 100 years would see worker incomes overtake capitalist incomes under these assumptions. Essentially, workers and capitalists would have swapped places in distributional terms. There are interesting

parallels here to the situation Keynes' characterised in the last chapter of the General Theory as ‘the euthanasia of the rentier’, in which a persis- tent oversupply of savings leads to a progressive decline in the rate of return on capital (Keynes, 1936).



5. Discussion


In his bestselling book, Capital in the 21st Century, French econo- mist Thomas Piketty has proposed a simple and potentially worrying thesis. Declining growth rates, he suggests, give rise to worsening inequalities. The hypothesis has not gone unchallenged. Some have taken issue with his theoretical approach (Taylor, 2014; Barbosa-Filho, 2014) whilst others have challenged empirical assumptions, particularly regarding the value of sigma (σ), the elasticity of substitution between labour and capital (Semieniuk, 2014; Cantore et al., 2014). The theoretical treatment of this elasticity by Barbosa-Filho (2014) is particularly interesting, as it indicates that



the results in this paper could be generalised without assuming a partic- ular form of production function.

Our own approach has been to stick relatively closely to Piketty's assumptions, and to explore the robustness of his conclusions when variations in key parameters are taken into account. What we have shown is that, under certain conditions, it is indeed possible for income inequality to rise as growth rates decline. However, we have also established that there is absolutely no inevitability at all that a declining growth rate leads to explosive (or even increasing) levels of inequality. Even under a highly-skewed initial distribution of ownership of produc- tive assets, it is entirely possible to envisage scenarios in which incomes converge over the longer-term, with relatively modest intervention from progressive taxation policies.

The most critical factor in this dynamic is the elasticity of substitu- tion, σ, between labour and capital. This parameter indicates the ease with which it is possible to substitute capital for labour in the economy as relative prices change. Higher levels of substitutability (σ N 1) do indeed exhibit the kind of rapid increases in inequality predicted by Piketty, as growth rates decline. In an economy with a lower elasticity of substitution (0 b σ b 1), the dangers are much less acute. The ease with which capital can be substituted for labour is thus an indicator of the propensity for low growth environments to lead to rising inequality.

More  rigid  capital–labour  divisions  on  the  other  hand  appear  to

reinforce our ability to reduce societal inequality.

From a conventional economic viewpoint, this might appear to be cold comfort. Lower values of σ are often equated with lower levels of development. As Piketty (2014a: 222) points out, low levels of elasticity characterised traditional agricultural societies. Other authors have suggested that the direction of modern develop- ment, in general, is associated with rising elasticities between la- bour and capital (Karagiannis et al., 2005). Antony (2009a) and Palivos (2008) both argue that typical empirical values of σ are less than one for developing countries and above one for developed countries. The suggestion in the literature appears to be that prog- ress comprises a continual shift towards higher levels of σ. But this contention embodies numerous ideological assumptions. In particular it seems to be consistent with a particular form of capital- ism that has characterised the post-war period: a form of capitalism that has come under increasing scrutiny for its potent failures, not the least of which is the extent to which it has presided over con- tinuing inequality (Davidson, 2013; Galbraith, 2013).




Fig. 7. a: Inequality reduction through progressive taxation. b: Convergence of incomes under progressive tax policy (g → 0; σ = 0.5).





The possibility of re-examining this assumption resonates strongly with suggestions in the literature for addressing the chal- lenge of maintaining full employment under declining growth. In our own work, for example, we have responded to this challenge by highlighting the importance of labour-intensive services both in reducing material burdens across society and also in creating em- ployment in the face of declining growth (Jackson, 2009; Jackson and Victor, 2011). The findings from the SIGMA model support this view. In fact, with growth and savings rates equal to those in Fig. 7, initial distributions of income and capital as assumed there, and con- stant labour productivity growth of 1.8% per annum, unemployment rises to over 70% (Fig. 8: scenario 1), a situation that would clearly be disastrous for any society.

Suppose, however, that labour productivity were not to grow continually. This could potentially lead to an important avenue of opportunity for structural change in pursuit of sustainability. In- stead of a relentless pursuit of ever-increasing labour productivity,


economic policy would aim to protect employment as a priority and recognise that the time spent in labour is a vital component of the value of many economic activities (Jackson, 2011). Increased employment opportunities would be achieved through a structural transition to more labour intensive sectors of the economy (Jackson and Victor, 2013). This would make particular sense for service-

based activities – for instance in the care, craft and cultural sectors –

where the value of the activities resides largely in the time people devote to them. In policy terms, such a transition would involve protecting the quality and intensity of people's time in the work- place from the interests of aggressive capital. Such a proposal is not a million miles from Minsky's (1986) suggestion that govern-

ment should act as ‘employer of last resort’ in stabilising an unstable


Scenarios 2 to 4 in Fig. 8 all describe a situation in which by the end of the run, labour productivity growth has declined to a point where it is very slightly negative. By the end of the scenario, labour productivity is




Fig. 8. Unemployment scenarios under declining growth.





declining in the economy — production output is becoming more labour intensive. Fig. 8 reveals that this decline in labour productivity growth is not in itself sufficient to ensure acceptable levels of unemployment. For higher values of σ, unemployment is still running dangerously high. But for lower values of σ it is possible not only to maintain but even to im- prove the level of employment in the economy, in spite of a decline in the growth rate to zero.

Up to this point, our analysis of the elasticity of substitution has been a broadly descriptive one. We have explored the influence of the elastic- ity of substitution between labour and capital on the evolution of in- equality (and employment) in an economy in which the growth rate declines over time. It would be wrong to conclude from this that we are able to alter this elasticity at will. Most conventional analyses

(Duffy and Papageorgiou, 2000; Pereira, 2003; Chirinko, 2008) assume that values of σ are given — an inherent property of a particular econo- my or state of development. Such analyses usually confine themselves to showing how allowing for a range of elasticity facilitates a better

econometric description of a particular economy than assuming an elas- ticity of 1. Our own analysis here also assumes that the elasticities them- selves are fixed over time. The production function in Eq. (20) is predicated precisely on this assumption.

There is however a tantalising suggestion inherent in this analysis that changing the elasticity of substitution between labour and capital offers another potential avenue towards a more sustainable macro- economy, and in particular a way of mitigating the pernicious impacts of inequality and unemployment in a low growth economy. Exploring that suggestion fully is beyond the scope of this paper, but is certainly worth flagging here. It would require us first to move beyond the CES production function formulation adopted here. The appropriate functional form for such an exercise would be a Variable Elasticity of Substitution (VES) production function. We note here that there is substantial justification and considerable precedent for such a function (Sato and Hoffman, 1968; Revankar, 1971). Antony (2009b) suggests that VES functions offer better descriptions of real economies than

either CES or Cobb–Douglas functions. Adopting such a function

would allow us to explore scenarios in which σ changes over time. An alternative approach might be to adopt an institutionalist framework such as the one proposed by Barbosa-Filho (2014).

We should also recall here our assumption that the rate of return to capital is equal to the marginal productivity of capital. As we remarked


earlier, this assumption only holds in markets conditions where capital is unable to use its power to command a higher share of income. Clearly, in some of the scenarios we have envisaged, this assumption may no longer hold. Where political power accumulates alongside the accumu- lation of capital, the danger of rising inequality is particularly severe and is no longer offset simply by changes in the economic structure. This question also warrants further analysis.

Finally, we note the potential for increased financialisation to exacerbate inequalities in the distribution of incomes and of wealth. A particularly interesting take on this is presented in the Credit Suisse' (2014) Global Wealth Report which identifies a positive feedback be- tween inequality and asset prices: a higher concentration of wealth tends to increase the propensity to save across the economy which in- creases the demand for equities (eg) and inflates asset prices, increasing inequality still further. A report by Nef (2014) sets out a range of poten- tially dangerous causal links between financialisation and inequality. Further exploring the impact of these links in a stock-flow consistent framework is one of the motivations for our own ongoing work (Jackson and Victor, 2015).

In summary, this paper has explored the relationship between growth, savings and income inequality, under a variety of assumptions about the nature and structure of the economy. Our principal finding is that rising inequality is by no means inevitable, even in the context of declining growth rates. A key policy conclusion concerns the need to protect wage labour against aggressive cost-reducing strategies to fa- vour the interests of capital. This measure would have the additional benefit of maintaining high employment, even in a low- or degrowth economy.




The authors gratefully acknowledge support from the Economic and Social Research Council (ESRC grant no: ES/J023329/1) for Prof Jackson's fellowship on prosperity and sustainability in the green economy ( which has made this paper possible and for support from the Ivey Foundation for Prof Victor. The paper has also benefitted from comments on the work by Karl Aiginger, Fanny Dellinger, Ben Drake, Armon Rezai, two anony- mous referees and several participants in a small working group of the WWWforEurope project.



Appendix 1. Initial Values for the SIGMA Model


Sources for data: see note 9.



Variable                                                                           Values             Units        Remarks


Initial GDP                                                                        1800               $billion UK GDP is currently around £1.6 trillion; Canada GDP is around CAN$1.9 trillion.

Initial national income                                                        1500               $billion  UK and Canadian NI are both around 17% lower than the GDP.

Initial capital stock K                                                           6000               $billion Based on the estimate of capital to income ratio chosen below.

Initial capital to income ratio β                                            4                                  Capital to income ratio in Canada is a little under 3; in UK it is higher at around 5. Initial income share of capital α                                                                40%                %             The wage share of income as a proportion of NI is around 60% in both Canada and the

UK and capital.

Initial savings rate s as percentage of national income            10%                %             The ratio of net private investment to national income in Canada was around 8% in 2012.

In the UK the number was somewhat lower.


Elasticity of substitution σ between labour and capital                   Varies



In theory σ can vary between 0 and infinity. Empirical values found in the literature typically range from 0.5 (Chirinko, 2008) up to around 10 (Pereira, 2003). A lower

value of 0.5 and upper value of 5 is sufficient to demonstrate divergent conditions here.


Population                                                                         50                  Million The population of Canada is 34 million; that of the UK just over 60 million.

Workforce as % of population                                               50%                %             Workforces in developed nations are typically between 45% and 55% of the population. Initial workers as % of population                                                  50%                %             Initially there is no distinction between workersand capitalists.

Initial % of wages going to workers                                      50%                %             Initially there is no distinction between workersand capitalists.

Initial % of capital owned by capitalists                                  50%                %             Initially there is no distinction between workersand capitalists. Initial  unemployment  rate                                                            7%                  %             Typical of both Canada and the UK over the last few years.

Distribution parameter a                                                       Varies                           This value is calibrated for each σ according to Eq. (17) at time t = 0.

Initial technology augmentation coefficient A0                                                   Varies                           This value is calibrated for each σ (and a) using the production function at time t = 0.

Initial growth rate g in reference scenario                             2%                  %             Growth rates (of GDP) in both the UK and Canada were slower than this in the aftermath

of the financial crisis and in the UK currently a little higher.

Initial growth in labour productivity in reference scenario    1.8%                     %             This value is consistent with a 2% rate of growth in the NI and the maintenance of a constant

employment rate when σ = 1.

Initial tax rates                                                                  25%                %             In the reference scenario, typical economy wide net taxation rates (as a percentage of

household disposable income) are applied to the incomes of both capitalists and workers.

Retained profit ratio                                                            010%              %             Default assumption is that retained profits are zero and firms' contribution to investment costs is equal only to the depreciation on capital.







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Wolff, E., Zacharias, A., 2007. Class structure and economic inequality. Levy Economic Institute Working Paper No 487. Levy Economics Institute, NY (Online at: http://

Does credit create a ‘growth imperative’? A quasi-stationary economy with interest-bearing debt


Contents lists available at ScienceDirect


Ecological Economics


journal homepage: con



Ecological Economics 120 (2015) 3248






Does credit create a growth imperative? A quasi-stationary economy with  interest-bearing  debt

Tim Jackson a,, Peter A. Victor b

a Centre for the Understanding of Sustainable Prosperity, University of Surrey, Guildford, UK

b Faculty of Environmental Studies, York University, 4700 Keele St, Canada




a r t i c l e          i n f o  


Article history:

Received 11 June 2015

Received in revised form 5 September 2015 Accepted 20 September 2015

Available online 22 October 2015



Growth imperative Credit creation Interest

Money creation

Stock-ow consistent model Austerity


a b s t r a c t  


This paper addresses the question of whether a capitalist economy can ever sustain a stationary (or non- growing) state, or whether, as often claimed, capitalism has an inherent growth imperative arising from the

charging of interest on debt. We outline the development of a dedicated system dynamics macro-economic model for describing Financial Assets and Liabilities in a Stock-Flow consistent Framework (FALSTAFF) and use this model to explore the potential for stationary state outcomes in an economy with balanced trade, credit cre- ation by banks, and private equity. Contrary to claims in the literature, we find that neither credit creation nor the

charging of interest on debt creates a growth imperative in and of themselves. This finding remains true even

when capital adequacy and liquidity requirements are imposed on banks. We test the robustness of our results in the face of random variations and one-off shocks. We show further that it is possible to move from a growth path towards a stationary state without either crashing the economy or dismantling the system. Nonetheless, there remain several good reasons to support the reform of the monetary system. Our model also supports cri- tiques of austerity and underlines the value of countercyclical spending by government.

© 2015 Elsevier B.V. All rights reserved.





1. Introduction


It has been argued that capitalism has an inherent ‘growth impera- tive’: in other words, that there are certain  features  of  capitalism which are inimical to a stationary state1  of the real economy. This argu-

ment has its roots in the writings of Marx (1867) and Rosa Luxemburg (1913) and there are good reasons to take it seriously. For instance, under certain conditions, the desire of entrepreneurs to maximise profits will lead to the pursuit of labour productivity gains in produc- tion. Unless the economy grows over time, aggregate labour demand

will fall, leading to a ‘productivity trap’ (Jackson and Victor, 2011) in

which higher and higher levels of unemployment can only be offset by continued economic growth.


*  Corresponding author.

E-mail address: (T. Jackson).

1 We use the term stationary state to describe zero growth in the Gross Domestic Product (GDP). We prefer here stationary to steady state, which is also widely used else- where to refer to a non-growing economy (Daly, 2014 eg), for several reasons. First, the

term steady state is employed in the post-Keynesian literature to describe a state of the economy in which the key variables remain in a constant relationship to each other (Godley and Lavoie, 2007:71) but this may still entail growth. A stationary state is used to describe a state in which both flows and stocks are constant, in which case there is no

growth. Second, the terminology of the stationary stateharks back to early classical

economists such as Mill (1848), emphasising the pedigree behind the idea of a non- growth-based economy. Finally, as one of our reviewers pointed out, the term steady state growth was commonly found in the literature (Hahn and Matthews, 1964: 781; Solow, 1970: Ch 1) prior to Daly's concept of a steady state economy.


Our concern in this paper is to address one particular aspect of the growth imperative: namely, the question of interest-bearing debt. A va- riety of authors have suggested that when money is created in parallel with interest-bearing debt it inevitably creates a growth imperative. To some, the charging of interest on debt is itself an underlying driver for economic growth. In the absence of growth, it is argued, it would be impossible to service interest payments and repay debts, which would therefore accumulate unsustainably. This claim was made, for in- stance, by Richard Douthwaite (1990, 2006). In The Ecology of Money,

Douthwaite (2006) suggests that the ‘fundamental problem with the

debt method of creating money is that, because interest has to be paid on almost all of it, the economy must grow continuously if it is not to collapse.’

This view has been influential amongst a range of economists critical of capitalism, and in particular those critical of the system of creation of money through interest-bearing debt. Eisenstein (2012) maintains that

‘our present money system can only function in a growing economy.

Money is created as interest-bearing debt: it only comes into being when someone promises to pay back even more of it’. In a similar vein, Farley et al. (2013) claim that the ‘current interest-bearing, debt- based system of money creation stimulates the unsustainable growth economy’ (op cit: 2803). The same authors seek to identify policies that ‘would limit the growth imperative created by an interest-based credit creation system’ (op cit: 2823).

The popular understanding that debt-based money is a form of growth imperative is intuitively appealing, but has been subject to

0921-8009/© 2015 Elsevier B.V. All rights reserved.




remarkably little in-depth economic scrutiny. A notableexceptionis a 2009 paper by Mathias Binswanger which sets out to provide an ‘expla- nation for  a  growth  imperative in modern  capitalist  economies,  which are also credit money economies’ (op cit: 707). As a result of the ability of commercial banks to create money through the expansion of credit, he claims (op cit: 724), ‘a zero growth rate is not feasible in the long run’. Binswanger  (2009)  finds  that  much  depends  on  the  destination  of

interest payments in the economy. If banks distribute all their profits (the difference between interest received and interest paid out) to households, then the ‘positive threshold level’ for growth can fall to zero. This condition is ruled out in his analysis, however, by the de-

mands of ‘capital adequacy’— the need to ensure a certain buffer against

risky assets on the balance sheet of commercial banks. This require- ment, underlined by many in the wake of the financial crisis (BIS, 2011) seeks to ensure that banks have sufficient capital to cover the

risk associated with certain kinds of assets (primarily loans). Binswang- er maintains that this requirement is ‘crucial for establishing the growth imperative’ (op cit: 713). By his own admission, however, Binswanger's paper ‘does not aim to give a full description of a modern capitalist econ- omy’. In particular, he notes (op cit: 711) that his model ‘should be dis- tinguished from some recent modelling attempts in the Post Keynesian tradition’ which set out to provide ‘comprehensive, fully articulated, theoretical models’ that could serve as a ‘blueprint for an empirical rep- resentation of a whole economic system’ (Godley, 1999: 394). A recent symposium on the growth imperative has contributed several new

perspectives on Binswanger's original hypothesis, but these papers also fall short of providing a full analysis of this kind (Binswanger, 2015; Rosenbaum, 2015).

In the current paper, we seek to address this limitation. Specifically, we aim to analyse the hypothesis that debt-based money creates a ‘growth imperative’ within a Stock-Flow Consistent (SFC) representa-

tion of the macro-economy. In the following section, we provide a brief overview of a systems dynamic model of the macro-economy, in- cluding both the real and the financial economy and describe the cali- bration of this model with empirically plausible data. Our principal aim is to test the ability of the model to provide for a stationary state. We also explore the stability of the model under one-off shocks and ran- dom fluctuations in consumer demand, and under different responses from government and commercial firms. Finally, we test the potential for transitions from growth states of the economy into stationary states and discuss the implications of these findings for capitalism and for the

‘growth imperative’.


2. Overview of the FALSTAFF Model


The analysis in this paper is based on our development (over the last four years) of a consistent approach to ‘ecological macroeconomics’. Our broad approach draws together three primary spheres of modelling in- terest and explores the interactions between them. These spheres are:

1)  the environmental and resource constraints on economic activity;

2) a full account of production, consumption, employment and public fi- nances in the ‘real economy’ at the level of the nation state; and 3) a comprehensive account of the financial economy, including the main interactions between financial agents, and the creation, flow and de-

struction of the money supply itself. Interactions within and between these spheres of interest are modelled using a system dynamics framework.

An important intellectual foundation for our work comes from the insights of post-Keynesian economics, and in particular from an ap- proach known as Stock-Flow Consistent (SFC) macro-economics, pioneered by Copeland (1949) and developed extensively by the late Wynne Godley and his colleagues.2  SFC modelling has come to the


fore in the wake of the financial crisis, because of the consistency of its accounting principles and the transparency these principles bring not just to an understanding of conventional macroeconomic aggregates like the GDP but also to the underlying financial flows and balance sheets. It is notable that Godley (1999) was one of the few economists who predicted the crisis before it happened.

The overall rationale of the SFC approach is to account consistently for all monetary flows between different sectors across the economy. This rationale can be captured in three broad axioms: first that each ex- penditure from a given actor (or sector) is also the income to another actor (or sector); second, that each sector's financial asset corresponds to some financial liability for at least one other sector, with the sum of all assets and liabilities across all sectors equalling zero; and finally, that changes in stocks of financial assets are consistently related to flows within and between economic sectors. These simple understand- ings lead to a set of accounting principles with implications for actors in both the real and financial economy which can be used to test the con- sistency of economic models and scenario predictions.

Building on these foundations we have developed a macroeconomic model of Financial Assets and Liabilities in a Stock and Flow consistent Framework (FALSTAFF), calibrated at the level of the national economy. The approach is broadly post-Keynesian in the sense that the model is demand-driven and incorporates a consistent account of all monetary flows. The full FALSTAFF model (Jackson et al 2015) is articulated in terms of six inter-related financial sector accounts: households, firms,

banks, government, central bank and the ‘rest of the world’ (foreign sec-

tor). The accounts of firms and banks are further subdivided into current and capital accounts in line with national accounting practises. The household sector can be further subdivided into two sectors in order to test the distributional aspects of changes in the real or financial economy.3

The FALSTAFF model is built using the system dynamics software STELLA. This kind of software provides a useful platform for exploring economic systems for several reasons, not the least of which is the ease of undertaking collaborative, interactive work in a visual (icono- graphic) environment. Further advantages are the transparency with which one can model fully dynamic relationships and mirror the stock-flow consistency that underlies our approach to macroeconomic modelling. STELLA also allows for an online user-interface (NETSIM) through which the interested reader can follow the scenarios presented in this paper and explore their own.4 Data collation and reporting are carried out in Excel.

For the purposes of this paper, we have simplified the FALSTAFF structure in order to focus specifically on the question of interest- bearing money. For instance, we assume balanced trade in this version of FALSTAFF and restrict the number of categories of assets and liabili- ties to include only loans, deposits, equities and government bonds. Fur- ther simplifications are noted at the relevant places in our full model description below. Fig. 1 illustrates the top-level structure of financial flows for the simplified version of FALSTAFF described in this paper.

The familiar ‘circular flow’ of the economy is visible (in red) towards

the bottom of the diagram in Fig. 1. The rather more complex surround- ing structure represents financial flows of the monetary economy in the banking, government and foreign sectors. If the model is stock-flow consistent, the financial flows into and out of each financial sector con- sistently sum to zero throughout the model run. So, for instance, the in- comes of households (consisting of wages, dividends and interest receipts) must be exactly equal to the outgoings of households (includ- ing consumption, taxes, interest payments and net acquisitions of finan- cial assets). Likewise, for each other sector in the model. These balances provide a ready test of consistency in the model.





2 See for instance: Godley, 1999, Godley and Lavoie, 2007, Lavoie and Godley, 2001. For an overview of the literature on SFC macroeconomic modelling, see Caverzasi and Godin, 2015.


We have used this subdivision to explore the implications of Piketty's (2014) hypoth- esis that inequality increases as the growth rate declines (Jackson and Victor, 2015).

4    The online model may be found at:




Fig. 1. An overview of the FALSTAFF stationary state model.



The broad structure of the FALSTAFF model is as follows. Aggregate demand is composed of household spending, government spending, and the investment expenditure of firms.5 The allocation of gross in- come is split between the depreciation of fixed capital (which is as- sumed to be retained by firms), the return to labour (the wage bill) and the return to capital (profits, dividends and interest payments).

Households' propensity to consume is dependent both on income and on financial wealth (Godley and Lavoie, 2007). The model also in- corporates the possibility of exploring two kinds of exogenous ‘shocks’

to household spending. In the first, a random adjustment is made to household spending throughout the run, within a range of plus or minus 2.5% from the predicted value. In the second, a one-off shock ei- ther reduces or increases spending by 5% over two consecutive periods early in the run. We use these exogenous shocks to test the stability of the stationary state under our default assumptions.

Household saving may in principle be distributed between govern- ment bonds, firms equities, banks equities, bank deposits and loans.6 Household demand for bonds is assumed here to be equal to the excess supply of bonds from government, once banks' demands for bonds are met. Household demand for equities is assumed to be equal to the


5  For simplicity, we assume for the purposes of this paper a balanced trade position in which exports are equal to imports and net trade is zero.

In the full FALSTAFF framework, household saving is allocated between a range of fi-


issuance of equities from firms and banks. Thus, households are the sole owners of equity in this model and the return on equities is limited to dividends received, since there are no capital gains in the model.7 The balance of household saving, once bond and equity purchases have been made, is allocated to paying down loans or building up deposits. If saving is negative, households may also increase the level of loans.

Firms are assumed to produce goods and services on demand for households, governments and gross fixed capital investment. Invest- ment decisions are based on a simple accelerator function (Jorgenson, 1963, Godley and Lavoie, 2007) in which net investment is assumed to be a fixed proportion of the difference between capital stock in the previous period, and a target capital stock determined by expected de- mand and an assumed capital-to-output ratio. A proportion of gross profits equal to the depreciation of the capital stock over the previous period is assumed to be retained by firms for investment, with net (ad- ditional) investment financed through a mixture of new loans from banks and the issuance of equities to households, according to a desired debt-to-equity ratio.

Government receives income from taxation and purchases goods and services (for the benefit of the public) from the firms sector. Taxa- tion is only levied on households in this version of the model, at a rate which provides for an initially balanced budget under the default values for aggregate demand. For the purposes of this paper, we explore three


nancial assets (and liabilities) including bank deposits, equities, pension funds, govern-                                      


ment bonds (and mortgage and loans), using an econometrically-estimated portfolio allocation model based on the framework originally proposed by Brainard and Tobin (1968).


7 This assumption is relaxed in the full FALSTAFF model, in which both equity prices and housing vary according to supply and demand. These assets are therefore subject to capital gains in the full model.




government spending scenarios: one in which government spending remains constant throughout the run, one in which government spend- ing plus bond interest is equal to tax receipts (i.e., an ‘austerity’ policy in which government balances the fiscal budget), and one in which gov-

ernment engages in a ‘countercyclical’ spending policy, increasing

spending when aggregate demand falls and decreasing it when aggre- gate demand rises. Government bonds are issued to cover deficit spending.

Banks accept deposits and provide loans to households and to firms, as demanded. Bank profits are generated from the interest rate spread between deposits and loans, plus interest paid on any government bonds they hold. Profits are distributed to households as dividends, ex-

cept for any retained earnings that may be required to meet the capital account ‘financing requirement’. This financing requirement is the dif- ference between deposits (inflows into the capital account) and the sum of loans, bond purchases and increases in central bank reserves (outgoings from the capital account). The central bank plays a very sim-

ple role in the stationary state version of FALSTAFF, providing liquidity on demand (in theformof centralbank reserves) to commercial banks in exchange for government bonds.

FALSTAFF provides for two regulatory policies that might reasonably be imposed on banks. First, the model can impose a ‘capital adequacy’ requirement in which banks are required to hold enough ‘capital’ to cover a given proportion of risky assets. Second, banks may be subject to a central bank ‘reserve ratio’ in which reserves are held at the central

bank up to a given proportion of deposits held on account. Some devel- oped countries (including the UK and Canada) no longer retain formal reserve ratios, leaving it up to the banks themselves to decide what re- serves to hold. However, we have included a default reserve ratio of 5% in order to test Binswanger's hypothesis that such requirements might lead to a growth imperative.

The capital adequacy requirement is supposed to provide resil- ience in the face of defaulting loans, as required for instance under the Basel III framework (BIS, 2011). In fact, we adopt as our starting

point the Basel III requirement that banks' ‘capital’ (the book value

of equity in the banks' balance sheet) should be equal to 8% of risk- weighted assets (loans to households and firms). To meet this re- quirement, banks in FALSTAFF issue equities to households. This has the effect of shifting deposits to equity on the liability side of the balance sheet and increasing the ratio of capital to loans. To bal- ance the balance sheet, banks purchase government bonds (conven- tionally deemed risk-free)   which together with central bank

reserves (also risk-free) provide for a certain proportion of ‘safe’ cap-

ital to balance against risky assets.

Our principal aim in this paper is to identify the potential for a sta- tionary state economy, even in the presence of debt-based money. In fact, it may be noted that our economy is almost entirely a credit money economy. No physical cash changes hands, and transactions are all deemed to be electronic transactions through the bank accounts of firms, household and government (and through the reserve account of the central bank). For the purposes of testing the role of credit crea- tion in the growth imperative, this simplification is clearly robust. We have also incorporated conditions on commercial banks appropriate for the testing of the overall hypothesis that interest-bearing debt leads to growth.





Though central to the real economy, and in particular the envi- ronmental impacts of production and consumption, we are less in-



be set exogenously in the model. The wage rate is assumed to follow any increase in labour productivity.8

Table 1 shows the financial balance sheet for the FALSTAFF ‘steady state’ model. As mentioned above, we have employed a rather simple

asset and liability structure for the purposes of this exercise in order to allow us to focus our attention on the question of interest-bearing debt. Households own firm equities Ef and purchase government bonds Bh. Balances are held either as deposits Dh or as loans Lh. Firms take out loans Lf or issue equities Ef in order to finance investment. Firms' surpluses can either be used to pay down loans or to increase firms deposits Df. In addition to the loans they provide to firms and households, commercial banks also hold government bonds Bb for cap- ital adequacy reasons and central bank reserves R for liquidity reasons. The central bank balances its reserve liabilities with government bonds Bcb purchased from banks on the secondary market. Govern- ments hold only liabilities in the form of bonds B.

The transaction flows matrix (eg Godley and Lavoie, 2007: 39) for FALSTAFF (Table 2) incorporates an account of the incomes and expen- ditures in the national economy, reflecting directly the structure of the system of national accounts. Thus, the first ten rows in Table 2 illustrate the flow accounts of each sector. For instance, the household sector re- ceives money in the form of wages and dividends from production firms and dividends and (net) interest from banks. Households spend money on consumption and on taxes. The balance between income and spend- ing represents the saving of the household sector. Note that the top rows of column 2 (firms' current account) represent a simplified form of the conventional GDP accounting identity:


C þ G þ I ¼ GDPe  ¼ GDPi  ¼ W þ P f  þ i f  þ δ                                               ð1Þ


where GDPe represents the expenditure-based formulation of the GDP, GDPi represents the income based formulation, and if represents the net interest paid out by firms.

The bottom five rows of the table represent the transactions in finan- cial assets and liabilities between sectors. So, for example, the net lend- ing of the households sector (the sum of rows 1 to 10) is distributed amongst five different kinds of financial assets in this illustration: de- posits, loans, government bonds, equities and central bank reserves. A key feature of the transaction matrix, indeed the core principle at the heart of SFC modelling, is that each of the rows and each of the columns must always sum to zero. If the model is correctly constructed, these zero balances should not change over time as the simulation progress. The accounting identities shown in Table 2 therefore allow for a consis- tency check, to ensure that the simulations actually represent possible states of the monetary economy.9


3. Analysis


The aim of this paper is to explore the hypothesis that the creation of money through interest-bearing debt necessarily creates a ‘growth im- perative’. The existence of one reasonable stationary state solution,

based on reasonable and consistent values for the various parameters would disprove the hypothesis. In pursuit of such a solution, we first run through the algebraic structure of the model.

Starting with the household sector, we can define the income Yh, of

households (in accordance with Table 2) as:


terested in this paper in the precise nature ofthe production process itself. Clearly, however, some aspects are important for our task. For instance, we need to establish the capital investment


Yh ¼ W þ Pfd þ  bd


þ iBh  þ iDh iLh                                                                                                                                ð2Þ


needs for production, since these are a core component of aggregate                                     


demand and determine both the level of financing for firms and the destination of household saving. The second major input to produc- tion is labour. Employment in FALSTAFF is assumed to take place via the firms sector and labour demand is calculated through a sim- ple labour productivity equation. Labour productivity growth can


The full version of FALSTAFF includes a model of wage bargaining and therefore allows us to consider the question of prices and inflation.

9    These identities are established in FALSTAFF via the accounting structure shown in Fig.

Error! Reference source not found., in such a manner that the stock associated with each monetary sector must always be empty. This structure therefore provides for a ready visu- al check on the consistency of the model.



Table 1

Financial balance sheet for the FALSTAFF stationary state economy.






Central bank



Net financial worth

Dh + E + Bh Lh

Lf Ef + Df

L + R + Bb D Eb

Bcb R



Financial Assets

Dh + E + Bh


L + R



R + D + L + B + E

Reserves Deposits









Loans Bonds











Financial Liabilities




Lf + Ef


D + Eb






R + D + L + B + E








Deposits Loans



















Our presentation of the financial balance sheet in Table 1 follows the format established in the National Accounts ( eg) rath- er than the presentation favoured by SFC theory (Godley and Lavoie, 2007: 32 eg). A numerical example of the financial balance sheet for FALSTAFF representing the initial state of the model is shown at Appendix 2.









where iBh = rBBh  is the interest paid on the stock of bonds held by





Remembering that households are the only owners of equity in this



households, iDh = rDD1 is the interest paid on households deposits





and iLh = rLLh   the interest paid by households on loans. Disposable in-



model, the household net worth NW


is equal (see Table 1) to:


come, Yhd, is given by:


Yhd   ¼ ð1−θÞYh                                                                                                                                                                                              ð3Þ


where θ is the rate of income tax on households, determined (below) by government's initial financing requirement. In allocating household income between consumption spending, C and saving Sh,

we adopt a consumption function of the form (Godley and Lavoie,


NWh  ¼ Dh þ Bh  þ ELh :                                                                                ð6Þ


Household saving is then given by:


S¼ YhdC:                                                                                                   ð7Þ


In this version of FALSTAFF we do not have households making fixed



2007 eg):


C ¼ α1 Yhde  þ α2 NWh






capital investments, and so the net lending NL





simply by:



of households is given




where α1 and α2 are respectively the propensity to consume from




¼ S :                                                                                                        ð8Þ


disposable income and the propensity to consume from wealth (both assumed constant for the reference scenario) and households' expected disposable income Yhde is given by a simple extrapolation of the trend over the previous period:



The next step in the model is to determine the allocation of net

lending between different assets and liabilities. In the full version of FALSTAFF (Jackson et al., 2014, Jackson et al 2015) we adopt a portfolio allocation function of the form originally proposed by Brainard and Tobin(1968)  andadaptedbyGodley  and Lavoie(2007) tofulfil


0          Yhd


hd    1


this task. For the stationary state version of the model, however, we


1 Y2

Yhde  ¼ Yhd                                                                       



assume simply that households purchase all equities issued by firms






1 @1 þ



hd                   A:                                                                ð5Þ



and absorb the bonds not taken up by banks (and the central bank).




Table 2

Transaction flows matrix for the FALSTAFF stationary state economy.



Households (h)

Firms (f)







Banks (b)








Bank (cb)

Gov (g)

Consumption (C)









Gov spending (G)









Investment (I)









Wages (W)









Profits (P)

+ Pfd + Pbd


+ Pfr


+ Pbr




Depreciation (δ)


+ δ






Taxes (T)









Interest on loans (L)






+ rlL-1





Interest on deposits (D)

+ rdDh


+ rdDf








Interest on bonds (B)

+ rbBh




+ rbBb



+ rbBcb




Change in reserves (R)






+ ΔR



Change in deposits (D)





+ ΔD




Change in bonds (B)







+ ΔB


Change in equities (E)



+ ΔEf


+ ΔEb




Change in loans (L)

+ ΔLh


+ ΔLf

















The change in household deposits is then determined as a residual according to:


where the depreciation, δ, of firms' capital stock K is defined by:


δ ¼ rδ K−1                                                                                                                                                                                                            ð18Þ



x    NLh                     f                                          b                  cb



ΔDh ¼ ma n(        −ΔE  −(ΔB−ΔB  −ΔB



; −Dh








:                       ð9Þ




for some rate of depreciation rδ (assumed constant).

One of the critical decisions that firms must make is how much to in-












So long as NLh −ΔEf −(ΔB −ΔBb −ΔBcb) ≥− D1, households do not need to take out loans. In the case where the supply of equities and the residual supply of bonds exceeds saving, households draw down deposits in order to purchase these assets. Where there are insuf- ficient deposits, ie where NLh −ΔEf −(ΔB −ΔBb −ΔBcb) b − D 1, then households will take out loans ΔLh according to:




vest in each year. We assume here a simple ‘accelerator’ model (Godley and Lavoie, 2007: 227 eg) in which net investment Inet is decided ac- cording to the difference between the actual capital stock at the end of the previous period K-1 and a ‘target’ capital stock Kτ sufficient to meet the expected demand for output, with a fixed capital to output ratio κ. Hence we have:

Inet  ¼ γ(KτK1 )                                                                                           ð19Þ






ΔLh ¼ ΔEf þ  ΔBΔBb ΔBcb



NLh Dh


:                                         ð10Þ




for some ‘accelerator coefficient’ γ, with 0 ≤γ≤ 1, and target capital


Coming next to the firms sector, we assume that this sector supplies











all the goods and services included in the GDP, so that firms' revenues are given by the left hand side of Eq. (1) plus any interest iDf = rDDf received on deposits. From these revenues, firms must pay wages W, distribute dividends P fd, and make interest payments iLf = rLL1 on loans. Wages are calculated according to:



W ¼ wLE;                                                                                                    ð11Þ


where the labour employed LE is given by:




stock Kτ given by:







Kτ ¼ κGDP ;                                                                                                ð20Þ



where GDPe, the expected GDP, is determined (as for disposable in- come) via a simple trend function of the same form as shown in Eq. (5). Gross investment I is then given by:


I ¼ Inet þ δ:                                                                                                    ð21Þ


We assume a funding model for firms in which firms cash flow or retained earnings is equal to the depreciation δ, so that profits, P fd,


LE ¼


η                                                                                                        ð12Þ


distributed as dividends, are equal to profits Pfnet of depreciation.11 In this case, the net lending of firms NLf is given by:


and η is the labour productivity of the economy at time t. Typically, in a capitalist economy, the labour productivity is deemed to grow


NLf  ¼ I







:                                                                                                ð22Þ


over time. If gη is the growth rate in labour productivity, then we can write:


gη t


Net borrowing (negative net lending) of firms is funded by a mixture

of loans ΔLf from banks and equity ΔEf sold to households. The exact split between debt and equity is determined by a desired debt to equity


η ¼ η0 e


;                                                                                                    ð13Þ


ratio ε, such that:



where η0 is the initial labour productivity, and it follows that:







W ¼ η egη t GDP:                                                                                           ð14Þ



We further assume that the wage rate w increases over time at the same rate as labour productivity. In other words, we suppose that workers are paid the marginal product of their labour.10 Wage rates are not suppressed by the power of capital (as might happen for in- stance when unemployment is high); nor do workers exert any upward


Lf  ¼ εEf :                                                                                                        ð23Þ


Assuming that historical debt and equity more or less satisfy this ratio, then firms would be expected to take out net loans ΔLfand issue new equities ΔEfin the same proportions so that:


ΔLf  ¼ εΔE f ;                                                                                                  ð24Þ






from which it is straight forward to show that: 1



pressure on wages (as might happen when unemployment is very low).

In this case it follows that:


w ¼ w0 egη t ;                                                                                                    ð15Þ


ΔLf  ¼

1 þ









and accordingly that wages W are given by:








ΔEf ¼




NLf :                                                                                   ð26Þ


w0 egη t





W ¼ η egη t GDP:                                                                                          ð16Þ



In other words it follows that wages W are a constant proportion w0


of the GDP. Firms' profits Pf(net of depreciation) are then given by:


ð1 þ εÞ


In the event that net investment is negative, ie when firms are in- clined to disinvest in fixed capital, then firms' net lending is positive. We assume first that firms use this cash to pay off loans. In the event that there are no more loans to pay off, firms save excess cash as de- posits with banks.



P f  ¼   1



GDPi þ i  f δ;                                                              ð17Þ


η0                                L                D



10  This assumption is relaxed in the full version of FALSTAFF.


11 It is in principle possible to relax this assumption, but it would immediately lead to positive net investment and accumulation of the capital stock. Since these provide condi- tions for growth in the real economy, they would detract from our desire to eliminate such conditions from the model, in order to test that aspect of the growth imperative that de- rives from interest-bearing money.




The banks sector in FALSTAFF is a simplified accounting sector whose main function is to provide loans ΔLf to (and where necessary to take deposits ΔDf from) firms and to take deposits ΔDh from (and where necessary provide loans ΔLh to) households. In order to meet liquidity needs, commercial banks keep a certain level of reserves R with the cen- tral bank, depending on the level of deposits held on their balance sheet. The additional reserve requirement ΔR in any year is given by:








where the last term is included to offset the purchase of banks bonds by the central banks to meet reserve requirements.

Whereas for firms, capital account positions are determined by the needs of the current account, in the case of banks, we derive the current account balances from the capital account positions, specifically we determine banks retained earnings (undistributed profits) from their fi- nancing needs. Banks income consists in the difference between interest received on loans and government bonds and the interest paid out on







ΔR ¼ ψ  Dh



þ D1


R1                                                                                                                                                ð27Þ


deposits.13 Hence, banks' profits P


are given by:



where ψ is the desired (or required) reserve ratio. Banks ‘pay for’ these reserves by ‘selling’ an equivalent value in government bonds to the central bank, thus depleting their stock of bonds by an amount

ΔBcb equal to ΔR, and increasing the stock of government bonds held by the central bank by the same amount.

To comply with capital adequacy requirements under the long-term targets set out under the Basel III accord, banks are required to hold cap- ital (equity) equivalent to a given proportion of risk-weighted assets. For the purposes of this paper we take the sum of risk-weighted assets to be equal to the sum of loans Lfand Lh to firms and households respec- tively. Banks' capital is defined by the book value of the banks sector eq- uity Eb according to:


Eb ¼ L þ R þ Bb D                                                                                      ð28Þ


where Bbare government bonds held by the banks' sector, D = Df + Dh, and L = Lf + Lh. The long-run Basel III requirement is then met by setting a target capital adequacy ratio φT, such that:




P  ¼ iL f   þ iLh  þ iBb iDh iD f :                                                                          ð34Þ






Banks' saving is equal to the difference between total profits Pband the profits Pbd distributed to households as dividends. Rather than spec- ifying a fixed dividend ratio to determine Pbd and calculating banks' sav- ing Sb from this, we determine instead a desired net lending NLb for banks, according to the financing requirements of banks' capital account and set the saving equal to this. Hence, we have:



NLb ¼ ΔLf þ ΔLh þ ΔBb                        −ΔDh ΔDf  ;                                                  ð35Þ

cap ad



and we can then determine banks' dividends, Pbd, according to:


Pbd  ¼ Pb Sb  ¼ Pb NLb :                                                                               ð36Þ


with NLb given by Eq. (35).






Finally, we describe the government sector accounts. The current ac- count elements14 in the Government's account are relatively simply expressed in terms of the equation:



φT  ¼


L  ¼ 0:08:                                                                                           ð29Þ




¼ S    ¼ TGiB ;                                                                                  ð37Þ




Assuming initial conditions in which this requirement is met, then the capital adequacy ratio is maintained by the banks' sector, provided that:


where taxes, T, are given by:


T ¼ θYh ;                                                                                                        ð38Þ






ΔEb ¼ φT LEb




:                                                                                         ð30Þ



and the interest, iB, paid on government bonds is given by:



In other words, banks' issue new equities (to the households sector)

equivalent to the shortfall between the required capital adequacy pro- portion of loans and the equity value in the previous period.12 It is


iB ¼ i h  þ i b  ¼ rB ( h




B                B                           B−1









þ B1




:                                                                ð39Þ


worth emphasising here that loans and deposits are determined by de- mand (from the household and firms sectors), reserves are determined by the reserve requirement and equities are determined by the capital adequacy requirement. The final discretionary element on the banks' balance sheet is government bonds, which we assume that banks will

hold in preference to reserves where they can – ie once the reserve

requirement is met – because they bring income from interest. The tar- get value of banks' bonds BbT can be determined from Eq. (28) as:


BbT  ¼ DRL þ Eb :                                                                                      ð31Þ


Note that no interest is included for government bonds owned by

the central bank, as profits from the central bank are assumed to be returned directly to the government. The capital aspect of the govern- ment account is simply a matter of establishing the level of government debt, through the change in the stock of outstanding government bonds, B, according to:


ΔB ¼ −NLg :                                                                                                 ð40Þ


When the government runs a fiscal deficit, the net lending, NLg, is negative leading to an increase in the stock of outstanding bonds. In



Or equivalently, using the reserve requirement to determine R and the capital adequacy ratio to determine Eb, we can write:


the event that government runs a fiscal surplus, NL

stock of outstanding bonds declines.


is positive and the


BbT  ¼ Dð1−ψÞ−Lð1−φÞ:                                                                            ð32Þ


Again assuming initial conditions meet this requirement, then banks target for holding government bonds is met, provided that:


A key feature of stock-flow consistent models is that they explicitly

satisfy a key condition that prevails in the macroeconomy, namely that sum of net lending across all sectors is equal to zero. In other words:


NLh þ NLf  þ NLb þ NLg ¼ 0:                                                                           ð41Þ






ΔBb ¼ BbT Bb



þ ΔBcb ;                                                                             ð33Þ



13 We omit here for simplicity interest paid on reserves. In the event that this was includ- ed in the model, it would simply represent a transfer from the central bank (essentially from government) to banks. We note here also that the banks sector does not pay wages


12    We assume in this version of FALSTAFF that households purchase all equities issued by

the banks sector and that the market value of equities so issued is determined by the book value of equity.


in FALSTAFF. These are deemed to be paid via the firms sector as are public sector wages.

14   In keeping with National Account conventions, the current and capital elements of the government sector are not shown in separate accounts in Table 2.




Or in other words, using Eqs. (7), (8), (22), (35) and (37) above, we should expect that:


Yhd CInet þ Pb Pbd þ TGi h i ¼ 0:                                                   ð42Þ


illustrate this stationary state solution with specific numerical values, check its evolution over time, and explore what happens when the sys- tem is pushed away from equilibrium.


B              B

4. Numerical Simulation


Noting that Y hd + T = Yh and using Eq. (2), it follows that:


W þ P fd þ ih i h  þ Pb i ¼ C þ G þ Inet :                                                   ð43Þ

D              L                               B


Since P fd = P fand noting that Pb can be expanded (Eq. (34)) as a sum of interest receipts (and payments), we can show that Eq. (43) can be rewritten as:


W þ P f  þ i f i ¼ C þ G þ Inet                                                                                                                                       ð44Þ



We select first a range of numerical values to initialise the variables in FALSTAFF as detailed in Appendix 1. Drawing from empirical data in Canada and the UK,15 we select values that could reasonably be taken to describe an advanced western economy. The initial GDP of $2 trillion is broken down between consumption (60% of GDP), government ex- penditure (20%) and gross investment (20%). We assume an initial cap- ital stock value of $6 trillion suggesting a capital-to-output ratio of 3. For

the economy not to be growing in real terms, this means that the depre-


L              D

ciation rate is approximately 7%, so that gross investment just covers the


or equivalently that:


W þ P f  þ i f  þ δ ¼ C þ G þ I                                                                         ð45Þ


which is precisely (see Eq. (1)) where we started from. The net lending condition is therefore a useful consistency check for the validity of the model as a whole and will be one of the aspects tested across different scenarios in the numerical simulations.

Having established the accounting identities and behavioural rela- tionships of the FALSTAFF model, we next need to determine some ini- tial values consistent with stationary (or quasi-stationary) solution. For the purposes of this exercise, this means that there should be no long-

term drivers of growth in the ‘real economy’. So, for instance, we

would expect no net accumulation of the productive capital stock K. Specifically this means setting the initial gross investment, I0, in produc- tive capital equal to the initial depreciation δ0:

I0  ¼ δ0  ¼ rδK0 ;                                                                                              ð46Þ


where rδis the depreciation rate and K0 denotes the value of the cap- ital stock at time t = 0. In addition, government spending is assumed not to grow over time and government debt does not accumulate over time. This means setting initial government expenditure G0 and the ini- tial household income tax rate T0 so that government achieves a fiscal balance:


G0 þ rBB0 ¼ T0 ;                                                                                             ð47Þ


where rB is the rate of interest on government bonds (assumed con- stant) and B0 is the stock of outstanding bonds at time t = 0. From Eqs. (46) and (47) it follows that:


NLf  ¼ NLg  ¼ 0;                                                                                             ð48Þ


depreciation of capital. The national income (GDP minus depreciation) is assumed to be split initially between wages (returns to labour) and profits (return to capital) in the ratio 60:40.

Firms' productive capital stock is assumed to be capitalised equally between debt ($3 trillion in loans from banks) and equity ($3 trillion in shares held by households). The accelerator constant γ in the invest- ment function is taken initially as 0.1.16 A smaller amount of equity ($887 billion) is invested in banks, sufficient to provide an initial rate of return on equity (banks dividends divided by the equity) equal to the rate of return on firms equity. In addition to equity holdings, house- holds are also deemed initially to hold $1 trillion in deposits and an equal amount in government bonds. Interest rates of 1% (on deposits), 2% (on bonds) and 5% (on loans) are set exogenously.17

A capital adequacy ratio for banks is set at 8% and the desired reserve ratio for banks holdings of central banks reserves is set at 5%. These pa- rameters in their turn determine the level of bond holdings by the banks, reserve holdings by banks and bond holdings by the central bank (equal to the reserve holdings of banks). The sum of bond holdings by households, banks and the central bank is taken as the initial stock of government debt. Using the exogenous bond interest rate, it is then pos- sible to calculate the initial interest burden on government which, to- gether with the exogenous initial government expenditure, must be met by taxation. Using households' total income, this enables us to cal- culate (see Eq. (50) above) a tax rate on households sufficient to ensure a balanced fiscal budget equal to the initial target government spending plus the interest rate on bonds held by households and by banks. For the parameters given above this turns out to be approximately 26%.

Finally, we assume a level of the workforce required to produce the output in the FALSTAFF economy with an initial unemployment rate of 7%, typical of advanced economies. From these initial values, we con- struct eight separate scenarios to test the hypothesis that positive inter- est rates lead to a growth imperative. The first six of these scenarios are

initialised using parameters consistent with a stationary state and are


0                     0

defined as follows:


and hence that:


NLh þ NLb ¼ 0;                                                                                              ð49Þ














0                                                                                                                                                                          0




For stationary state solution, as Godley and Lavoie (2007: 73) point out, the net lending NLh of the household sector must also be equal to zero. Otherwise, it is clear to that NW h would either rise or fall, leading to rising or falling consumption. This means that the initial value C0 of household consumption must be equal to the initial disposable income  Yhd. This can be satisfied by choosing a tax rate θ at which Eq. (47) is satisfied. Since T0 = θ0Yh, we can use Eq. (2) to deduce that:


G0 þ rBB0



    Scenario 1: the model is run using the values established in Appendix 1 with no adjustments;

    Scenario 2: the model is run with a small (max ± 2.5%) random vari-

ation to consumer demand in each year;

    Scenario 3: the model is run using a small (5%) one-off shock (reduc- tion) in consumer demand in year 20;

    Scenario 4: government responds to Scenario 3 with a ‘strict’ austerity

policy in which the initial fiscal balance is maintained, no matter what;

    Scenario 5: firms respond to Scenario 3, with a version of Keynes'


15  Data for the Canadian economy may be found in the Cansim online database: http://


θ0  ¼ W


P fd


bd            Bh


Dh          Lh :                                                      ð50Þ; and for the UK economy on the Of-


0 þ  0  þ P0   þ i0  þ i0  i0


In short, conditions (46) to (50) define an initial state consistent with a stationary solution to the model. In the following section, we



ce for National Statistics online database: html?nscl=Economy#tab-data-tables.

16  See for example Tutulmaz and Victor, 2013.

17   As with most of the variables in the model, these values can be selected by the user.




Fig. 2. GDP on an expenditure basis (Scenario 1).



‘animal spirits’, in which more is invested when things are going well (ie when expected output rises) and less when they are going worse (ie  when  expected  output  falls);

    Scenario 6: governments respond to the conditions in Scenario 5, by

engaging in counter-cyclical spending.



Finally, we explore a scenario in which the economy is initially growing and then moves towards a stationary state.


    Scenario 7: government expenditure is assumed to grow at 2% per annum for the first three periods of the run; this growth rate the de- clines to zero over the subsequent decade and remains at zero for the rest of the run.



The results of Scenario 1 are illustrated in Figs. 2 and 3. Fig. 2 shows the GDP on an expenditure basis. The graph itself is not particularly in- teresting other than that it confirms, as expected, that with a suitable choice of initial values, a stationary state economy is possible. More in- teresting for our purposes in this paper is that this result is obtained from an economic model with interest-bearing debt, and in spite of the fact that banks are subject to both a capital adequacy requirement and a reserve ratio requirement.

Since net lending in the stationary state is equal to zero for all sec- tors, it is to be expected, and Fig. 3 confirms, that the net financial worth of each of the FALSTAFF sectors remains unchanged over the pe- riod of the run. Fig. 3 also illustrates one of the fundamental accounting identities of the stock-flow consistent model, namely that the sum of all financial assets and liabilities across all sectors, ie the net financial worth of the economy as a whole, is zero.

It is not possible in the space of this paper to illustrate, although the reader can verify for themselves in our online model, that the results in Figs. 2 and 3 do not depend on specific values chosen for the interest rates on deposits, loans and bonds;18 nor do they depend on the specific values chosen for capital adequacy or reserve ratio; although, not sur- prisingly, the steady state tax rate (Eq. (50)) changes when these pa- rameters are altered. In short, the results of Scenario 1 appear to

indicate that there is no categorical ‘growth imperative’ embedded in


18 Explicitly, these results were tested for deposit rates between 0 and 10% and for loan rates between 0 and 15% (with an interest rate spread between 0% and 10%). The interest- ed reader may check for themselves using our online model at: FALSTAFF_steadystate.


the structure of a credit-based money system with interest-bearing debt in the capitalist economy.

Our next aim is to test the robustness of this finding, once values de- part from the equilibrium values defined at t = 0. Scenario 2 subjects consumer demand to a small random variation within a range of

± 2.5% of the initial value, C0, of consumer demand. In other words, within each period consumer spending is assigned a random value in the range [0.975C0,1.025C0]. All other initial values for both stocks and flows are the same as in Scenario 1. The impact on the growth rate from this variation is shown in Figs. 4 and 5.

Although Fig. 4 shows considerable variation in the short term growth rate (within a range of less than ±1%) it is clear that the long-run growth rate is still around zero. Certainly there is no obvious systematic expan- sion of the economy, even though the net lending positions of the differ- ent sectors (Fig. 5) vary considerably over the run. Again, variations in deposit, loan, and bond rates and in the capital adequacy requirement and the reserve ratio make no appreciable difference to this long-term trend, or indeed to the amplitude of the variations around it. We could de- scribe the economy illustrated in Figs. 4 and 5 as a quasi-stationary-state economy with a long-run average growth rate of zero. Notice that the sum of net lending remains zero across the run, in spite of the variation in net lending in individual sectors. This is an indication that the model is working consistently, and reflecting correctly the accounting identities that must hold in any real economy. Though the pattern looks rather dra- matic, notice that the amplitude of the variations in net lending is not high

— less than 0.5% of the GDP in most cases.

Scenario 3 tests the resilience of the stationary state solution under a single consumption shock. Consumer demand is depressed by 5% in pe- riods 20 and 21 of the scenario, and thereafter returns to the initial value. All other values are unchanged. The results of this scenario are il- lustrated in Figs. 6 and 7. As might be expected, Fig. 6 shows a sharp downward spike in the growth rate, followed by a sharp upward spike

(above the long-run zero growth rate) as ‘normal’ consumption behav-

iour resumes in period 22. Thereafter, the growth rate rather quickly returns to something close to zero, but tends to oscillate around zero for some time, approaching zero asymptotically as the economy ‘settles

down’ again.

The net lending behaviours of different sectors (Fig. 7) show a simi- lar pattern, with rather high initial movements away from the equilibri- um position, which tend to attenuate over time as the growth rate flattens towards zero. Fig. 7 reveals that some individual sectors switch from being net lenders to net borrowers and back again several times during this process of readjustment. As in Fig. 5, only the banking sector maintains a net lending position very close to zero. In spite of having the




Fig. 3. Financial net worth of FALSTAFF sectors (Scenario 1).




flexibility to retain some proportion of profits in order to meet financing needs (Eq. (32)), this turns out not to be necessary most of the time, with the outlay on new loans, bonds and reserve requirements more or less matching the inflow of new deposits. The sector most negatively affected in the early years following the shock is the government sector which experiences a dramatic increase in the deficit.

At this point, the government is faced with some critical choices about how to respond. Instinctively, of course it may want to respond to the increased deficit either by increasing taxation or by reducing

spending. In Scenario 4, we test the outcome of strict ‘austerity’ policy

on the shock introduced in Scenario 3. Fig. 8 provides a graphic illustra- tion of how things can go wrong if governments cut back spending too fast in order to reduce a fiscal deficit. In this (admittedly extreme) case, the government insists on trying to return the fiscal deficit to zero, resulting in a spectacular collapse of the FALSTAFF economy.

It is also useful to think a little about the potential responses of firms to the sudden change in circumstances represented by the one-off con- sumption shock established in Scenario 3, in particular in relation to their investment behaviour. The investment function introduced in


Eq. (19) sets out a behavioural response by firms to changes in expected demand, depending on two factors:

Inet  ¼ γ(KτK1 ):                                                                                          ð51Þ


The first factor (represented by the expression in brackets in Eq. (51)), is the perceived shortfall or surplus in capital stock, deter- mined on the basis of a target capital stock required to meet the expect- ed demand. If expected demand rises, the target capital will be higher than the capital in the previous year, and so the expression in brackets will be positive and firms will seek to undertake net investment. In this case, gross investment is greater than the depreciation of the capital stock. If expected demand falls, the expression in brackets will be nega- tive and firms will seek to disinvest. In this case the gross investment is less than the depreciation of the capital stock.

The second key element in Eq. (51) is the ‘accelerator coefficient’, γ,

which is a measure of the desired ‘speed of adjustment’ undertaken by

firms in response to changes in demand. Higher values of γ will increase the responsiveness of firms to a change in demand, lower values of γ





Fig. 4. Growth rate under random uctuations in consumer demand (Scenario 2).




Fig. 5. Net lending under random uctuations in consumer demand (Scenario 2).



Fig. 6. Growth rate after a one-off negative consumption shock (Scenario 3).




will decrease the responsiveness. A higher value for γ can be thought of as capturing a high degree of what Keynes (1936) called ‘animal spirits’; that is: a greater willingness amongst entrepreneurs to invest when times are good, and a lower willingness to invest when things are not

going so well. To test the impact of animal spirits on the FALSTAFF econ- omy, in the wake of a consumption shock, we looked at the impact of in- creasing the γ coefficient (from 0.1 to 0.15) throughout Scenario 5. The result is illustrated in Figs. 9 and 10.

We assume in this exercise that animal spirits are a long-term feature of the economy and do not change over time. So the new value of γ is ap- plied from the beginning. Interestingly, this has no impact while the econ- omy is in a stationary state. This is because the capital shortfall (the expression in brackets in Eq. (51)) is zero during this time. Consequently the value of the accelerator coefficient is irrelevant. Once the economy is shocked out of its stationary state however, things are different: the higher coefficient immediately sets in motion a cyclical pattern of increas- ing amplitude, with every sign of becoming unstable.19 In the real world such a dynamic would lead to numerous uncomfortable consequences,


19   In fact, running the model to 200 periods reveals a collapse in stability.


including high unemployment, price instability, and widely fluctuating net lending positions (Fig. 10).

A core concept in Keynesian and post-Keynesian economics is the idea of countercyclical spending; that is: the idea that governments can play a useful stabilising role in an unstable economy by increasing spending when output is falling and reducing spending when output is rising. In Scenario 6, we explore the impact of countercyclical spending as a possi- ble policy response to the situation in Scenario 5. Following the consump- tion shock (as in Scenario 3) in an economy with high animal spirits (as in Scenario 5), the government in the FALSTAFF economy responds by in- creasing spending at the same rate as the expected aggregate demand is falling when the economy is in recession and reducing spending at the same rate as expected aggregate demand is rising when the economy is growing. The consequences on the growth rate are illustrated in Fig. 11, where we also show for comparison the growth rates for scenarios 3 and 5. Remarkably, a countercyclical spending response more than com- pensates for the destabilising influence of animal spirits following the de- mand shock. The FALSTAFF economy is returned more quickly to a quasi- stationary state than in scenario 3, with only slight long-run deviations from zero growth and no net accumulation.




Fig. 7. Net lending after a one-off negative consumption shock (Scenario 3).




Fig. 8. Economic collapse from strict austerity after a negative shock (Scenario 4).





Finally, we explore a scenario in which the economy is initially growing, in other words where the economy starts away from the sta- tionary equilibrium. We are interested to find out if the ability to achieve a stationary state depends on a particular starting position, in which the sectors are all in balance, with no net lending and zero growth. What would happen if the economy was already growing, and accumulating debts or assets in different sectors? Is it still possible to move towards a stationary or quasi-stationary state from these con- ditions with positive interest rates? Or is such an economy destined to either grow for ever or become unstable?

In Scenario 7 (Figs. 12 and 13), we suppose that the initial growth rate in government spending is 2% per annum, and that the initial ex- pected growth in output, disposable income and household wealth is also 2% per annum. We assume that these conditions pertain for the first three periods of the scenario, but that after this point, government begins slowly to reduce the growth rate in spending until by period 13 of the run, it has declined to zero. Fig. 12 illustrates this transition in terms of the GDP for the FALSTAFF economy. It appears that the transi- tion to a (quasi-) stationary state is indeed possible; but it takes some


time before the perturbations induced by ‘animal spirit’ responses die down. These oscillations are also visible in the net lending positions (Fig. 13). Again it can be shown, that countercyclical spending by gov- ernment  dampens  the  oscillations  associated  with  this  transition.20

Fig. 12 also shows that the pattern of transition in the GDP is echoed in the money supply. It is interesting to note, however, that the oscilla- tions in the money supply lag those in the GDP, suggesting that in the FALSTAFF economy at least, changes in the money supply are driven by what is happening in the real economy, rather than the other way around. Increased output demands increased loans from firms creating a higher level of deposits from households. Fig. 13 also shows the veloc- ity  of  circulation  of  money  which  is  calculated  endogenously  in




20 If growth in the economy is declining faster than the desired growth rate, government spending is increased above the target rate. If it is declining slower than the desired rate, spending growth is reduced faster than the target rate. See Scenario 8 in the online version of the model at:




Fig. 9. The growth rate after a demand shock with animal spirits (Scenario 5).



Fig. 10. Net lending after a demand shock with animal spirits (Scenario 5).





FALSTAFF through the ratio of GDP to the money supply.21 Because money supply lags demand, the velocity of money increases initially in  order  to  maintain  aggregate  demand.


5. Discussion


The aim of this paper was to explore the potential for a stationary (non-growing) economy in the presence of credit creation and interest-bearing debt. To this end, we presented a stock-flow consistent

(SFC) system dynamics model (FALSTAFF) of a hypothetical closed



requirements on banks to maintain a minimum positive capital adequa- cy ratio and sufficient central bank reserves. Contrary to claims in the lit- erature, we found no evidence of a growth imperative arising from the existence of a debt-based money system per se.

In fact, we presented a variety of scenarios which exemplified quasi- stationary states of various kinds, and which offered resilience from in- stability in the face of random fluctuations, demand shocks, and exag-

gerated ‘animal spirits’. We also simulated a transition from a growth-

based economy towards such a state. None of the scenarios were sensi- tive to modest changes in the values for interest rates on deposits, loans



economy with private ownership and credit-based money. Behavioural


and government bonds.


Perhaps most significantly from our point of


aspects of the model include the propensity to consume out of both in- come and wealth, a simple accelerator model of firms' investment, and


view, these conclusions are not changed by imposing demands on

banks to maintain a given capital adequacy ratio or to hold a given






21 Since prices are not included in the model, conventional formula Mv= pT, where M is the money supply, v the velocity of money, p the price level and T the volume of transac- tions, reduces to MV=GDP. GDP is given by the model; M is taken as the sum of deposits and reserves and V can then be calculated as V =GDP/M.


22 A sensitivity analysis was conducted in FALSTAFF for values of the interest rate on loans between 0 and 15%, and on bonds and deposits between 0 and 10%. Slight increases in the amplitude of oscillations was observed at higher interest rates, under conditions of shock. But the conclusions observed in this paper still held.




Fig. 11. Stabilising influence of countercyclical spending after a demand shock with animal spirits (Scenario 6).





ratio of central bank reserves to bank deposits. The only scenario in which instability led to economic collapse was the one in which we im- posed a ‘strict’ austerity policy in response to a negative shock to con- sumer demand. In this case, it was the austerity policy, rather than the existence of debt, that crashed the model.

The fact that the charging of interest on its own does not lead to a growth imperative could perhaps have been inferred from the realisa- tion that the only interest payments which contribute directly to the GDP are the net interest payments of firms. All other interest payments turn out to be transfers between sectors and neither restrict nor en- hance aggregate demand in themselves. Clearly net interest payments of firms will increase if firms' loan requirements expand; and this will happen if, for instance, firms decide to expand investment. But in this case, growth is driven directly by expansion in aggregate demand, not by the charging of interest in itself.


Slightly more surprising perhaps is that neither capital adequacy nor reserve ratio requirements change this conclusion. At the heart of the growth imperative hypothesis lies the claim that banks' cap-

ital is somehow money that is ‘withheld’ from the economy. Admati

and Hellwig (2013:6) claim that this view arises from a misunder- standing of banks' capital as “cash that sits idly in the bank's tills without being put to work in the economy”. In their view, this is a deliberate misrepresentation propagated by the banking lobby to “confuse regulatory debate” (Ibid). Irrespective of this point, our analysis confirms that these regulatory initiatives act neither to

reduce the potential for debts to be serviced nor to expand aggre- gate demand.

The exercise in this paper is subject to a number of caveats and lim- itations. In the first place, we assumed a ‘closed’ economy, in which net trade was zero throughout. In addition, prices were excluded from the






Fig. 12. GDP and the money supply during transition to a stationary state (Scenario 7).




Fig. 13. Net lending positions during transition to stationary state (Scenario 7).





model, meaning that inflationary or destabilising price effects could not be explored. In Scenarios 1 to 6, we deliberately chose values for key variables such that real economy aggregates were not introducing expansionary effects. For instance, the model assumes no demographic changes which might require a rise in government expenditure even for a non-expanding population. Taxation is initially set so that government debt does not accumu- late. Firms financing behaviour is determined in such a way as not to accumulate capital assets beyond those deemed necessary to satisfy expected demand. There is no attempt to model housing investment and house price inflation, both of which may well in- troduce expansionary dynamics into the economy. Some of these assumptions can be relaxed by the user in the online version of the model. Others are the subject of ongoing exploration (Jackson et al 2015).

It should be noted, in particular, that we have not included certain microeconomic behaviours which might be expected to lead to specifically both to a heightened monetary expansion and also to aggregate demand growth or perhaps instability. For instance, it is clear that competitive (positional) behaviour by firms through profit maximisation could expand investment (particularly when finance is cheap) in order to stimulate de- mand (Gordon and Rosenthal, 2003). Neither do we attempt here to model Minsky-like behaviour in which progressive over-confidence amongst lenders leads to an expansion of credit, over-leveraging and eventual financial instability (Minsky, 1994, Keen, 2011).

It is also worth pointing out that, in spite of the findings in this paper, there area number ofgood arguments against private interest-bearing debt as the main means of creation (and destruc- tion) of the money supply. As a wide variety of authors have pointed out,23 this form of money can lead to unsustainable levels of public and private debt, increased price and fiscal instability, speculative behaviour in relation to environmental resources, greater inequality




23 Useful critiques of debt-based money can be found in Sigurjónsson, 2015, Daly, 2014, Wolf, 2014, Farley et al., 2013, Jackson and Dyson, 2012, Huber and Robertson, 2000, as well as the ground-breaking, early work from Douthwaite (1990). The idea of eliminating banks' ability to create money can be traced to Frederick Soddy (1931); for a useful histor- ical overview see Dittmer, 2015.


in incomes and in wealth, and a loss of sovereign control of the money system. We are therefore firmly of the opinion that monetary reform is an essential component of a sustainable economy. We re- gard the current study as an important way of distinguishing where effort should be placed in transforming this system. Specifi- cally, the results in this paper suggest that it is not necessary to elim- inate interest-bearing debt per se, if the goal is to achieve a resilient, stationary or quasi-stationary state of the economy.

It is also worth reiterating that, aside from the question of interest-bearing money, there exist several other incentives to- wards growth within the architecture of the capitalist economy. We have elucidated some of these incentives elsewhere (Jackson, 2009, Victor, 2008, Jackson and Victor, 2011). They must be taken to include, for instance: profit maximisation (and in particular the pursuit of labour productivity growth) by firms, asset price specula- tion and consumer aspirations for increased income and wealth. Some of these mechanisms also lead to potential instabilities in the capitalist economy. Many of them are reliant on the existence of credit-based money systems. Minsky (1994), perhaps most famously, has shown how cycles of investment and speculation, built around debt-based money, can lead to endemic instability. But this logic does not entail that interest-bearing money, in and of itself, creates a growth imperative.

Interestingly, the exercise in this paper has shown that, in spite of these incentives, a transition to a stationary economy from a growth- based economy is theoretically possible. We have illustrated in particu- lar the role of countercyclical spending by government in smoothing that transition. Encouragingly, we have shown that it is possible to get from a growth-based economy to a quasi-stationary state without ei- ther destabilising the economy or dismantling the concept of interest- bearing debt.




The authors gratefully acknowledge support from the Economic and Social Research Council (ESRC grant no: ES/J023329/1) for Prof Jackson's fellowship on prosperity and sustainability in the green econ- omy ( which has made this work possible. The present paper has also benefitted from a number of constructive com- ments (including some detailed discussions on the behaviour of banks) from Herman Daly, Ben Dyson, Graham Hodgson, Andrew Jack- son, Bert de Vries, and three anonymous referees.



Appendix 1

Initial values for FALSTAFF scenarios.

Sources for reference values: see note 16.


Variable                                                    Values        Units                Remarks


Initial GDP                                                 2000           $billion             UK GDP is currently around £1.6 trillion; Canada GDP is around CAN$1.9 trillion.

Initial consumer spending C                           1200           $billion             Assumes consumer spending is approximately 60% of GDP, typical for advanced western economies Propensity to consume from wealth (α2)                                 0.034                           We assume a small propensity to consume from wealth equivalent to $200 billion, consistent with

empirical data.

Propensity to consume from income (α1)            0.83                                Calculated as the ratio of non-wealth consumption ($1 trillion) to initial disposable income Initial government spending G                                                   400          $billion             Assumes government spending of 20% of GDP

Initial gross investment I                                400          $billion             Assumes investment of 20% of GDP

Initial depreciation                                        400          $billion             Assumes that gross investment equals depreciation.

Initial depreciation rate                                      6.67% %                     Chosen so that depreciation is equal to gross investment. Typical rates in advanced economies are around 68% Initial National Income                                          1600           $billion             Calculated by subtracting depreciation from GDP.

Initial wages (W)                                           960          $billion             Assumes labour's share of income is around 60% of the national income, typical in both Canada and the UK Initial profits (P)                                                                 640          $billion             Calculated by subtracting labour's share of income from the National income

Initial capital stock (K)                                 6000           $billion             Based on the chosen estimate of capital to income ratio Initial capital to income ratio                                                3                                Ratio in Canada is a little under 3; in UK around 5.

Initial investment accelerator (γ)                        0.1                              Typical range for advanced economies: 0.080.15

Initial firms debt Df                                                                         3000           $billion             Capitalisation split equally between debt and equity Initial firms' loans Lf                                                                                                          1000           $billion             Included  for completeness

Initial firms equity Ef                                                                      3000           $billion             Capitalisation split equally between debt and equity

Initial banks equity Eb                                                                        320          $billion             Calculated as the difference between banks' assets and liabilities other than equities Initial household deposits Dh                                                                                                  3000           $billion             Consistent with the assumption that (broadly speaking) loans are equal to deposits Initial household loans Lh                                                                                                         1000           $billion             Included for completeness

Initial household bond holdings Bh                                      1000           $billion             Leads to a debt-to-GDP ratio close to current levels Interest rate on deposits                                                    1%          %                     Typical of current values

Interest rate on government bonds                   2%          %                     Typical of current values Interest rate on loans                                                 5%          %                     Typical of current values

Initial reserve ratio                                        5%           %                     High by pre-crisis standards; low by post-crisis standards. Initial banks reserves R                                                    200          $billion             Chosen for consistency with reserve ratio

Initial central bank bonds Bcb                                                  200          $billion             Chosen for consistency with capital adequacy ratio Banks capital adequacy ratio                                    8%           %                     Consistent with Basel III banking regulations

Initial banks bonds Bb                                                                       120          %                     Consistent with chosen capital adequacy ratio, taking into account banks' reserve holdings. Initial government debt B                                      1320           $billion             Equal to the total of household, bank and central bank bond holdings

Initial household tax rate                               26%          %                     Calculated from initial household income at a level that will lead to a zero fiscal balance for government Initial unemployment rate                                        7%           %                     Typical of both Canada and the UK over the last few years.

Initial workforce                                             21.5        Million             Workforce is typically 45%55% of population.

Initial labour productivity                                   1          $m GDP/emp Consistent with initial GDP delivered by the initial workforce at the given unemployment rate.




Appendix 2

Initial balance sheet for FALSTAFF scenarios.







Gov                                  Totals

Net Financial Worth









–                                     12,840




–                                     4000



–                                     4000



–                                     3320





–                                     1320



–                                     200






1320                                 12,840



–                                     4000




–                                     4000




–                                     3320


1320                                 1320



–                                     200





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