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Does credit create a ‘growth imperative’? A quasi-stationary economy with interest-bearing debt
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
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
Stock-ﬂow 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.
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: email@example.com (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 state” harks 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
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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
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
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.
4 The online model may be found at: http://www.prosperitas.org.uk/falstaff_steadystate.
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.
6 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-
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
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
8 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.
Financial balance sheet for the FALSTAFF stationary state economy.
Net ﬁnancial worth
Dh + E + Bh − Lh
− Lf − Ef + Df
L + R + Bb − D − Eb
Bcb − R
Dh + E + Bh
L + R
R + D + L + B + E
Lf + Ef
D + Eb
R + D + L + B + E
Our presentation of the ﬁnancial balance sheet in Table 1 follows the format established in the National Accounts (http://stats.oecd.org/Index.aspx?DataSetCode=SNA_TABLE720 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 = rDD− 1 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 E−Lh : ð6Þ
Household saving is then given by:
Sh ¼ Yhd−C: ð7Þ
In this version of FALSTAFF we do not have households making ﬁxed
C ¼ α1 Yhde þ α2 NWh
capital investments, and so the net lending NL
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
this task. For the stationary state version of the model, however, we
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).
Transaction ﬂows matrix for the FALSTAFF stationary state economy.
Gov spending (G)
+ Pfd + Pbd
Interest on loans (L)
Interest on deposits (D)
Interest on bonds (B)
Change in reserves (R)
Change in deposits (D)
Change in bonds (B)
Change in equities (E)
Change in loans (L)
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
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) ≥− D− 1, 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(Kτ−K−1 ) ð19Þ
ΔLh ¼ ΔEf þ ΔB−ΔBb −ΔBcb
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 = rLL− 1 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,
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
over time. If gη is the growth rate in labour productivity, then we can write:
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
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 −
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−
GDP−i f 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
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
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:
L ¼ 0:08: ð29Þ
¼ S ¼ T−G−iB ; 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 L−Eb
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
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 D−R−L 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 −C−Inet þ Pb −Pbd þ T−G−i h −i b 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.
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 b ¼ C þ G þ Inet : ð43Þ
D L B
W þ P f þ i f −i f 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-
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
deﬁned as follows:
and hence that:
NLh þ NLb ¼ 0; ð49Þ
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
Dh Lh : ð50Þ
www5.statcan.gc.ca/cansim/home-accueil?lang=eng; and for the UK economy on the Of-
0 þ 0 þ P0 þ i0 þ i0 −i0
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: www.prosperitas.org.uk/ 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
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(Kτ−K−1 ): 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 ﬂuctuations in consumer demand (Scenario 2).
Fig. 5. Net lending under random ﬂuctuations 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: http://www.prosperitas.org.uk/falstaff_steadystate.
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.
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 (www.prosperitas.org.uk) 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.
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
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 6–8% 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: 0.08–0.15
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.
Initial balance sheet for FALSTAFF scenarios.
Net Financial Worth
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