Sustainability: Science, Practice and Policy ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/tsus20 The role of interest in the unsustainability of growth: analytical findings using an accounting model Jeroen van den Bergh & Ivan Savin To cite this article: Jeroen van den Bergh & Ivan Savin (2023) The role of interest in the unsustainability of growth: analytical findings using an accounting model, Sustainability: Science, Practice and Policy, 19:1, 2262830, DOI: 10.1080/15487733.2023.2262830 To link to this article: https://doi.org/10.1080/15487733.2023.2262830 © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group Published online: 16 Oct 2023. Submit your article to this journal Article views: 54 View related articles View Crossmark data Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=tsus20 Sustainability: Science, Practice and Policy 2023, VOL. 19, NO. 1, 2262830 https://doi.org/10.1080/15487733.2023.2262830 Research Article The role of interest in the unsustainability of growth: analytical findings using an accounting model Jeroen van den Bergha,b,c and Ivan Savina,d,e Institute of Environmental Science and Technology, Universitat Autònoma de Barcelona, Barcelona, Spain; bICREA, Barcelona, Spain; a School of Business and Economics & Institute for Environmental Studies, Vrije Universiteit Amsterdam, Amsterdam, The c Netherlands; dESCP Business School, Madrid campus, Madrid, Spain; eGraduate School of Economics and Management, Ural Federal University, Yekaterinburg, Russia ABSTRACT ARTICLE HISTORY In the context of the long-standing debate on growth-versus-environment, notably the Received 18 June 2021 possibility that serious environmental policies will slow down growth, the question has been Accepted 21 September raised if interest can be compatible with zero growth. We develop a simple accounting model 2023 that describes the value added of the financial sector being positively associated with interest KEYWORDS income. This allows us to derive formally that interest is compatible with zero growth for both Interest; limits to growth; simple and compound interest. The findings indicate that on its own, interest or compound post-growth; steady-state interest does not add to the growth of gross domestic product (GDP). What matters instead economy; environment is whether savings – be it from interest or other income – are invested productively or not. In other words, the condition for non-growth is that interest income is either directly spent by the creditor or indirectly by the debtor, rather than being invested in capital expansion, education, or innovation. Such investments would result in a more productive economy generating economic growth. These findings generalize, and add transparency to, previous studies which used more complicated models involving particular theoretical assumptions about the functioning of the macroeconomy. Introduction 2016). In this article, we develop an accounting model to analyze how interest affects economic growth. Two There is increasing concern that the pace of growth in claims about interest are sometimes conflated in the industrialized economies is environmentally unsustain- literature (e.g., Cahen-Fourot and Lavoie 2016, 167; able or that serious environmental policies will slow Berg, Hartley, and Richters 2015, 13); namely, whether down growth. This claim has renewed attention to the it is positive simple interest or the compounding of question: is lending at interest compatible with a sus- interest, that is the lending of income from interest (or tainable non-growing economy? The common wisdom interest income), that is incompatible with a stationary was that no, it is not. Drawing on Frederick Soddy’s economy. We will therefore devote attention to both (1926) work, various authors have argued that there is simple and compound interest. a conflict between an economy with positive interest Let us begin by defining some terms. One textbook rates, where debt can grow exponentially, and a real definition states that “[w]hen money is invested con- economy that is subject to environmental and resource tinuously, it earns compound interest, meaning that limits (e.g., Daly 1980; Martinez-Alier 1987; Farley interest is earned on past interest” (Samuelson and et al. 2013). In the light of increasing awareness of the Nordhaus 2009, 522). Another book defines com- macroeconomic consequences of environmental and pound interest as “an arrangement in which interest is resource constraints (Victor 2010; van den Bergh and paid not only on the original deposit but on all previ- Kallis 2012; Roth 2017), a handful of recent ecological ously accumulated interest” and distinguishes it from macroeconomic models have, however, found that “simple interest, in which interest is paid only on the positive interest rates can be compatible with a original deposit” (Frank et al. 2015, 493, emphasis in non-growing economy as long as there is no net sav- original). Compounding of interest often occurs in ing in the economy (Berg, Hartley, and Richters 2015; savings accounts, where the interest income earned by Jackson and Victor 2015; Cahen-Fourot and Lavoie the creditor in one period is lent, often to a different CONTACT Jeroen van den Bergh jeroen.bergh@uab.es Institute of Environmental Science and Technology, Universitat Autònoma de Barcelona, Barcelona, Spain © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent. 2 J. VAN DEN BERGH AND I. SAVIN debtor, in the next period. Since the term “compound The remainder of this article is organized as fol- interest” is often associated with a single fixed loan or lows. The next section describes the model and per- savings account, to avoid any misunderstandings, we forms an analysis with it. We then discuss our results use a slightly different term “compounding of interest” in the context of the aforementioned macroeconomic to denote a broader interpretation in a macroeconomic models that have shown that a non-growth economy context of multiple creditors, debtors, and a (possible) can be compatible with positive interest. The final combination of expanding or contracting loans. section presents our conclusions. The literature also pays attention to the stationar- ity of the economy. Godley and Lavoie (2007, 73) define a stationary economy as one in which “there A debtor-creditor accounting model is no change in financial stocks, that is, there is no Background saving.” With the latter, they mean that net saving in the economy is zero, which does not prevent that We develop a simple accounting model with a debtor some individuals can save and others can compen- (borrower) and a creditor (lender) and use it to sate this by consuming more than their income. examine two scenarios, namely where the creditor From a post-growth perspective, the most important spends income from interest payments by the debtor, aspect of a stationary economy is that gross domes- and where she lends it. The debtor receives income tic product (GDP) does not increase, hence Jackson from selling her productive output and any money and Victor’s (2015, 32) emphasis that the term “sta- she borrows, and her expenditures consist of her tionary state” describes an economy in which there purchases, the interest she pays on previous loans, is zero growth in the flow of GDP. However, zero and any repayment of the loan principal. GDP growth does not necessarily imply a stationary Correspondingly, the creditor receives income from economy since other stocks and flows may be chang- interest payments and any loan repayments, and her ing, so here we use the term zero growth to denote outgoings consist of her purchases and any expan- specifically an economy with no growth in GDP sion of the loan. (that may or may not also be stationary). An important element of our model is that Previous studies have assessed that interest-bearing income from interest is not part of GDP, but the debt per se is not inherently incompatible with a sta- value added of the financial sector is. Essential for tionary economy. For example, Jackson and Victor our finding is that in each year value added of the (2015, 46) say that the results in their article “suggest financial sector is positively associated with interest. that it is not necessary to eliminate interest-bearing Possibly, such association may vary over time but for debt per se if the goal is to achieve a resilient, station- a healthy financial sector, it seems pertinent that the ary or quasi-stationary state of the economy.” Similarly, long-term association is positive. In other words, a Cahen-Fourot and Lavoie (2016. 163) conclude that “a higher interest rate leads to higher value added and positive interest rate [is] compatible with a full sta- little debt not being repaid. Some question whether tionary economy.” Likewise, Richters and Siemoneit’s the financial sector creates value added, but we side (2017, 114) abstract states that their conclusion is that with those who think it does, despite problems in “interest-bearing debt-money with private banks does estimating it, as for other service sectors. According not lead to an “inherent” growth imperative.” to Haldane and Madouros (2011), the productive The contribution of the current article is to strip value and contribution to the GDP of the financial all the unique theoretical assumptions of the previ- sector lies in the management of risk. In particular, ous models to achieve a bare-bones accounting banks screen the productive potential of borrowers, model that offers a transparent tool for assessing while lenders remunerate banks in return.1 the connection between interest and growth. Since previous studies addressed the issue using rather complex models with many assumptions and numer- The model ical simulations, it has not always been clear what Equation (1) describes the balance of income and assumption was causing what result precisely, or expenditure of the debtor: how general the patterns obtained were. Instead, our accounting model is parsimonious, avoiding Yd ,t + Et = Cd ,t + rLt −1 + γ Ft + Rt (1) unnecessary behavioral, institutional, or macroeco- nomic assumptions. This approach allows us to where Yd ,t , Et , Cd ,t , r , Lt , γ , Ft , Rt ≥ 0 denote labor obtain a more general and clearer perspective on income, the expansion of the loan, consumption by the relationship between interest and growth, and the debtor, the fixed interest rate on loans, the total thus verify findings of previous models. size of the loan, fraction of cost of financial services Sustainability: Science, Practice and Policy 3 paid by the debtors, financial-sector value added, Scenario 1 – simple interest due to consuming and (partial or whole) repayment of the loan, at income from interest time t.2 Here we consider the case that the creditor con- We define the financial-sector value added Ft as sumes income from interest net of financial service positively associated with interest payments while cost, that is, does not lend it out to the debtor. not larger than these (captured by β): According to Equation (4) this means that rLt −1 − (1 − γ )Ft =Cc ,t, which combined with Equation Ft β rLt (0 < β < 1) = (2) (2) indicates that the net expansion of the loan is zero, or Et − Rt = 0. According to Equation (5) then The cost of these services is divided between the = Lt L= L0, with L0 the initial loan. In other words, t −1 debtor (γ Ft) and creditor ((1−γ )Ft) with 0 ≤ γ ≤ 1. the loan is constant over time, and simple interest Then total income is equal to Y= T ,t Yd ,t + Ft. Profits applies. From Equation (2) we then obtain that in the financial sector are consumed by its owners: Ft = β rL0 is constant. We abstain from growth factors like education and technical innovation, which CF ,t = Ft (3) means the debtor’s labor income is stationary or that Yd ,t = Yd for all t. Then Equations (1), (4), and (5) Since only debtors engage in the production of can be respectively written as: non-financial activities, Yd ,t can also be interpreted as Yd = Cd ,t + rL0 + γ Ft (6) the value of non-financial firms. Next, the balance of income and expenditure for the creditor is as follows: rL0 = Cc ,t + (1 − γ ) Ft (7) rLt −1 + Rt = Cc ,t + (1 − γ ) Ft + Et (4) Lt − Lt −1 = 0 (8) with Cc ,t ≥ 0 denoting consumption by the creditor. From these equations we can derive GDP (YT ,t) Equation (5) describes the change in the size of according to the expenditure approach as the sum of the the loan: three types of consumption (since there are no invest- Lt − Lt −1 =Et − Rt (5) ments, government expenditures, imports, and exports): with L0 ≥ 0 being the initial loan, which has been YT ,t = Cc ,t + Cd ,t + CF ,t = Yd − (γ + (1 − γ ))Ft + Ft = Yd originally saved by the creditor for the purpose of (9) lending. The above equations result in the following Hence, we find that if the creditor consumes and accounting matrix of the economy, underpinning its thus does not lend her income from interest, then only stock-flow consistency in line with Godley and simple interest arises in the model. The net expansion Lavoie (2007): of the loan is zero, and simple interest applies to the Non-financial Financial Debtors Creditors firms firms Total existing loan. The same amount of interest is paid each Consumption −C d ,t −C c ,t C d ,t + C c ,t + C F ,t −C F ,t 0 period. Total consumption in the economy then equals Interests −rLt−1 rLt−1 0 labor income which is constant over time. In other Bank fees −γ Ft −(1− γ )Ft Ft 0 words, lending/borrowing, even via a financial sector Profits and Yd ,t -Yd ,t 0 that charges for services, only leads to a reshuffling and dividends Change in 0 not an increase of money. Hence, simple interest does Et − Rt −(Et − Rt ) loan not translate into, or require, a rising total income (or Total 0 0 0 0 0 GDP). In other words, a non-growing economy can be Note that we do not need to address further consistent with interest per se. issues of stationarity/stability as our model does not include capital accumulation, labor-productivity Scenario 2 – compound interest due to improvements (through education or learning), tech- lending of income from interest nological innovation, or other factors that might cause growth. The reason is that it is just an account- Now we alter Equation (4) to reflect the case where ing model. the creditor does not spend the interest income on 4 J. VAN DEN BERGH AND I. SAVIN consumption but lends it out at interest. It means level, because of individuals’ own choice or because Cc ,t = 0, Et > 0 and Rt = 0.3 This translates into a con- banks evaluate the respective debtors as incapable of tinuous expansion of the loan to the debtor. paying higher interest. Another view stresses other Equations (1), (4), and (5) then become: behavioral aspects, namely that debtor and creditor are myopic, resulting in an increase of the debt until Yd ,t + Et = Cd ,t + rLt −1 + γ Ft (10) interest payments become unaffordable for the debtor (in which case they will ultimately die and stop borrowing). More factors and viewpoints are rLt −1= (1 − γ ) Ft + Et (11) discussed in Strunz, Bartkowski, and Schindler (2017) who conclude that the literature (both within mainstream and heterodox schools) is divided about Lt − Lt −1 = Et (12) whether such an imperative exists. Anyway, if the monetary supply were to increase, without an equiv- Combining Equations (10) and (11) gives: alent increase in production and consumption (eco- nomic growth), this would translate into increasing Yd = Cd ,t + (γ + (1 − γ ))= Ft Cd ,t + Ft (13) prices or inflation, and hence a rise in nominal but not real GDP. Since we do not model prices, this Using this result, we can derive GDP as: falls outside the scope of our analysis. YT ,t = 0 (Yd − Ft ) + Ft = Cc ,t + Cd ,t + CF ,t =+ Yd (14) Comparison with previous ecological macroeconomic models Hence, GDP is also constant in the case of com- pound interest. In other words, a non-growing econ- Here we relate our findings to previous results from omy can be consistent with compound interest. the ecological macroeconomic models mentioned in Next, combining Equations (2), (11), and (12) the first section. Richters and Siemoneit (2017) have gives a solution for Lt: presented a detailed review and stability analysis of these models; they also examine two models by t Godley and Lavoie (2007), which although not con- 1+ r  1+ r  Lt = Lt −1 =   L0 (15) structed for the purpose of examining interest 1 + (1 − γ ) β r  1 + (1 − γ ) β r   income still yield relevant insights. They all follow Godley and Lavoie’s (2007, 73) definition of a sta- This equation shows that the size of the loan is tionary economy as one in which there is no saving ever increasing at an exponential rate which takes because this would imply a change in stocks. To the form of compounding by a factor that increases achieve a stationary state, consumption must there- in the interest rate and decreases in the cost of fore equal disposable income (Jackson and Victor financial services. Note, though, that this increase 2015, 39; Berg, Hartley, and Richters 2015, 13; approaches zero if (1−γ )β is close to one (but it Cahen-Fourot and Lavoie 2016, 165). By considering always remains slightly smaller than one as the case that not all interest income is consumed, we 1 − γ ≤ 1 and β < 1). From the debtor’s point of view instead can examine in a transparent way what hap- the compounding occurs because they pay interest pens if the creditor does not spend (all) the interest on borrowed interest income from the previous income on consumption but lends it out at interest. period, which is added to the principal loan in each We find that this is compatible with a non-growing period. From the creditor’s point of view the com- economy. pounding results because they are paid interest on In other words, interest per se is theoretically their lent interest income from the previous period. compatible with a non-growing economy, contrary The size of the loan is ultimately limited by the to some earlier arguments (e.g., Douthwaite 2000). money supply in the economy. But if Equation (9) is Our model outlined above confirms this more gen- to hold true, this supply must adapt and increase – erally and analytically by minimizing the number which has been called a “monetary growth impera- of theoretical assumptions. We have shown that tive” (Strunz, Bartkowski, and Schindler 2017). There both simple and compounding interest – regardless are different views on this point. One perspective is of whether creditors spend or lend out interest that debt growth is limited by behavioral factors income – are compatible with zero growth. (which are not part of the accounting model). In Moreover, this is under the condition that value other words, an extension of the loan may be added of the financial sector is proportional to stopped once consumption reaches the subsistence interest payments. Sustainability: Science, Practice and Policy 5 In the three recent ecological macroeconomic from earning interest upon their interest income by models (Jackson and Victor 2015; Berg, Hartley, and ensuring that household consumption equals their Richters 2015; Cahen-Fourot and Lavoie 2016), the disposable income. Jackson and Victor (2015, 29) basic mechanism for avoiding compounding is the further explain that “For a stationary state solution, same as in our simple model: creditor consumption. as Godley and Lavoie (2007, 73) point out, the net In other respects, these models are much more com- lending of the household sector NLh0 must also be plex, including a government sector that taxes and equal to zero.” So, to reach a stationary state where spends, and a differentiation between households no sectors have increasing stocks, households must and firms. These models show that if one subset of not be saving; and without saving there can be no households is saving, with output at a stationary lending of interest income. Though the results of level, the other sectors are facing a steadily rising their simulations are robust to various shocks and debt. Hence, they have as a condition for zero variations, and even to the transition from a grow- growth that there is no saving. Our model is consis- ing to a stationary state, compounding of interest is tent with this, but shows that also if there is savings, impossible in that stationary state. in terms of lending out of interest income, zero Berg, Hartley, and Richters (2015) aggregate the growth is feasible. banking sector, the central bank, and the govern- To clarify key differences further, Table 1 com- ment sector; firms in the industry sector pay interest pares the types of agents between our approach and on loans to the government, which pays interest to previous models. In Jackson and Victor’s (2015) households. Firms distribute all profits to house- model, the government pays interest to the central holds. Unlike Jackson and Victor, Berg et al. assume bank which returns all profits to the government, so no immediate consumption out of interest and profit such loans are effectively interest free. Firms pay all income at all, but instead that all household con- post-depreciation income to households. They write sumption is out of wealth and wages. Examining that “We assume a funding model for firms in which their model to establish the parameter space within firms’ cash flow or retained earnings is equal to the which a stock-flow equilibrium is reached, the depreciation, so that profits, distributed as dividends, authors conclude that “[t]hough our model shows are equal to profits net of depreciation,” explaining that positive interest rates do not necessarily imply in a footnote that relaxing this assumption “would exponential growth of government liabilities, this immediately lead to positive net investment and result crucially depends on consumption decisions accumulation of the capital stock” providing growth by households” (Berg, Hartley, and Richters 2015, (Jackson and Victor 2015, 37, mathematical notation 13). Specifically, in order to remain in a stationary removed). Banks also pay out all income from inter- state, taxes and consumption must be sufficiently est to households. Those households consume all of high to avoid household deposits increasing expo- their post-tax income, with government taxation set nentially as the “[f]lows of interest payments from to ensure that consumption is equal to disposable the government accumulate” (Berg, Hartley, and income. Hence, firms do not retain profits, and Richters 2015, 13). As in Jackson and Victor (2015), banks do not retain interest income – both pay them when the model is in a stock-flow equilibrium, the out to households. In turn, households are prevented total income of households equals taxes and con- sumption, so no interest income is ever lent at inter- est. This level of consumption prevents the problem Table 1. Our model compared with previous models. of compounding of interest occurring in their model. Who receives Who pays Cahen-Fourot and Lavoie (2016) present a sim- Model Sectors interest interest Ours Creditors Creditors pler static model and find, as they state in their Debtors Debtors abstract, that “a positive interest rate [is] compati- Binswanger Firms Firms Households ble with a full stationary economy” (163). As in (2009) Banks Banks Jackson and Victor (2015) and Berg, Hartley, and Jackson and Households Households Households Firms Firms Firms Richters (2015), banks and firms do not retain Victor (2015) Banks Banks Banks their income but pay all income out as dividends Central bank Central bank Government Government to individuals, who do not lend but consume Berg, Hartley, Households Households Households this income. and Richters Industry Industry (2015) Government Government Government (+ banking) (+ banking) (+ banking) Cahen-Fourot Households Households Conclusion and Lavoie Firms Firms (2016) Banks Banks In this article, we have aimed to clarify the debate Government Government on the compatibility of interest with a sustainable 6 J. VAN DEN BERGH AND I. SAVIN non-growing economy. We developed a simple Notes accounting model to show that both interest per se 1. Wang (2011) discusses the problems associated with and compounding of interest, due to lending income empirically estimating the exact value added of the fi- from interest against interest, are compatible with nancial sector and argues that current figures may zero growth. In other words, even if (at least some) overestimate it. These estimates have grown since creditors lend a part of their interest, or even if World War II from 2 to 8% for the United States, and banks receive a fee for connecting debtors and cred- since 1970 from 5 to 9% for the UK (den Haan 2011). 2. Note that the cost for mediating services by banks itors, this does not itself translate into aggregate is additional to the interest payment – the latter income growth in the economy. We formally showed goes to the creditor. In other words, F is not paid these results using a simple and transparent account- out of interest payment but is correlated with it. ing framework. Our main insight is that even if Alternatively, one could subtract the mediation cost interest income is not directly spent by the creditor from the interest payment so that the creditor gets less. But this would not change the essence of the but lent out, the result is a stationary economy. The model. reason is that interest income is then spent by the 3. Repayment is zero as it does not make sense to ex- debtor. In other words, the key condition for our pand the loan on one hand (Et > 0) and repay it on finding is that interest income must ultimately be the other hand (Rt > 0). In other words, if Et > 0 this spent – rather than being invested to create a more implies logically Rt = 0. And reverse, if Rt > 0 then productive economy that translates into economic Et = 0 holds. Of course, one could argue that each expansion creates a separate deposit that is also sep- (GDP) growth. arately paid back, but this does not undo the gen- An explanation for this finding, that interest and eral approach outlined here. One might also consid- zero growth are compatible, is that (compound) er Et as the net expansion and Rt as the net interest payments and income themselves are not repayment. productive in terms of creating value-added and thus contributing to GDP. Only when interest income is invested productively (e.g., in capital, education, Acknowledgements or innovation) can it add to GDP growth. Our This work contributes to the “María de Maeztu” model findings show that on its own, interest or Programme for Units of Excellence of the Spanish Ministry compound interest does not add to GDP growth. To of Science and Innovation (CEX2019-000940-M). We are grateful to Tilman Hartley, Giorgos Kallis, and an anony- see it differently, the fundamental reason for GDP mous reviewer of this article for discussions and com- growth can be regarded as increases in labor pro- ments which helped us considerably improve the model ductivity. This can only come about through the and refine the findings. mentioned investments in capital (machines), educa- tion (human capital), and innovation (indirectly affecting the productivity of machines and educa- Disclosure statement tion). This issue goes beyond our basic model but No potential conflict of interest was reported by the authors. could be further investigated developing a model with investment in productive capital along the lines Funding of Binswanger (2009). As previous macroeconomic models addressing This work was supported by Horizon 2020 [882314]. this matter (sometimes as a side-issue) are rather complex, it is not always clear which of their ORCID assumptions was exactly causing what outcome. Instead, our model is limited to accounting relation- Jeroen van den Bergh http://orcid. ships, avoiding unnecessary behavioral, institutional, org/0000-0003-3415-3083 or macroeconomic assumptions. This approach Ivan Savin http://orcid.org/0000-0002-9469-0510 results in a clear and fundamental perspective on the link between interest, income, and growth. In References addition, previous studies often use numerical simu- Berg, M., B. Hartley, and O. 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