Debt-led growth and its financial fragility Joana David Avritzer December 30, 2020 Abstract This paper discusses the financial sustainability of demand-led growth models. We assume a supermultiplier growth model in which household consumption is the autonomous component of demand that drives growth. We show that for positive rates of growth the model converges to an equilibrium where worker households are accumulating debt and not wealth. We also show that when the economy is growing at a rate that is positive, but not too high, the dynamics of the model also implies that households will not be able to service their debt at equilibrium. We then conclude that this household debt-financed consump- tion pattern of economic growth generates an internal dynamic that leads to financial instability. Keywords: household wealth dynamics, debt-financed consumption, growth and financial fragility; JEL Classification: E11, E12, E21, O41. 1 1 Introduction This paper discusses the financial sustainability of demand-led growth models, in which household debt-financed consumption is the autonomous component of de- mand that drives growth. It is composed of three sections, besides this introduction and a conclusion. In the first section we present a literature review of demand-led growth theories focusing on those models that incorporate household debt-financed consumption. We discuss the models presented both by the neo-Kaleckian and the su- permultiplier theory. We see that while in the neo-Kaleckian model the debt-financed component of consumption must be determined by current income, as investment is autonomous, in the supermultiplier literature credit-financed consumption can be autonomous from current income. These models also allow us to think about the financial sustainability of these patterns of growth from the perspective of the work- ing households as they accumulate debt so as to maintain consumption. In the second section of this paper we present our own model for the consumption function of the working household. We argue that workers consumption is deter- mined by a wealth target, as is suggested in Dutt (2006). However, we also suggest that their wealth target cannot be fully explained by their current income. Conse- quently, their consumption becomes partially autonomous from current income. We then develop a surpermultiplier model of growth in which household consumption, which can be financed through debt or accumulated wealth, becomes the autonomous component of demand that drives growth. Finally, in the third section of this paper we discuss the long run dynamics of our model. We find that for positive rate of economic growth the long run stability of our model require households to accumulate debt. We also find that for positive, but not too high, rates of economic growth, the dynamics of our model leads households 2 to accumulate a level of debt is not financially sustainable to them as their debt servicing becomes higher than their wages. 2 Demand-led growth and household debt-financed consumption The neo-Kaleckian approach assumes that capitalist investment is autonomous from current income as it follows the function described in Bhaduri and Marglin (1990). In these models household debt dynamics has been incorporated through the defini- tion of a workers consumption function that allows them to consume beyond their income as they accumulate debt. However, since this approach assume an exogenous investment function, this accumulation of debt must always become, for some reason or another, determined by current income. Dutt (2005, 2006) suggests that worker’s consumption, CW , and capitalists consump- 1 tion, CΠ, is given by the following two equations : dD CW = (1 − π)Y − rD + ; dt (1) CΠ = (1 − s)(πY + rD) Where Y is income, r is the interest rate, π is profit share, s is the fraction of income that household save and D is the stock of debt. It is also assumed that household accumulate a stock of debt that is given by a desired level of new borrowing, which is then determined by current income: dD (2) dt = B = Bd = β[(1 − π)Y − rD] 1The notation of the model has been slightly modified from the original contribution for consis- tency of notation through out the paper 3 Where β is the borrowing to net income ratio. Since the accumulation of new loan is a function of workers current income, total consumption becomes entirely determined I by current income and we can then assume that capital accumulation, K , follows a typical Kaleckian function as developed by Bhaduri and Marglin (1990). Another attempt of incorporating household debt-financed consumption into a neo-Kaleckian framework has been done by Setterfield and Kim (2016, 2017, 2018). In their model total income Y is divided into: Y = WP N + WSαN + Π (3) Where WP is the real wage of production workers, N is the number of production workers employed, WS is the real wage of supervisory workers, α < 1 denotes the necessary ratio of managers to production workers and Π denotes total profits. It is further assumed that WS = φWP , supervisor work get a constant portion of production workers. Additionally, total consumption, C, is given by2: _ C = CW + CR + D; _ T D = β(C − CW ); β > 0; T C = ηCR − !s;!s = tΠ; (4) CW = cW WP N; CR = cπ[φαWP N + (1 − t)Π + rDR] Where CW is consumption by working households, CR is consumption by rentier households and D_ is the borrowing by working households to finance additional consumption. Household borrowing is then determined by a targeted level of con- 2The notation of the model has been slightly modified from the original contribution for consis- tency of notation through out the paper. 4 sumption, CT , which, in its turn is determined by η, the emulation (keeping up with the Joneses) effect, minus the !s, social wages (social welfare system). Finally, DR = D − DW is the part of workers’ debt that is owned by the rentiers households for which they must pay an interest rate r. Palley (2010) and Pariboni (2016) emphasize that both models above require that B I D = K , in other words, that the stock of capital and the stock of debt grow at the same rate. This means that the pace of total consumption (induced plus credit financed) must be determined by the rate of capital accumulation. In Dutt (2005, 2006) this is done through the assumption that the desired level of borrowing Bd is determined by current income, as Bd = b[(1 − σ)Y − rD]. In this way the demand B I for loans grow in line with income and output and condition D = K is satisfied. In the model of Setterfield and Kim (2016, 2017, 2018) we must also have that the rate of accumulation determines the rate of growth of aggregate demand. This is done through assuming an endogenous consumption target. 2.1 The supermultiplier approach Under the supermultiplier approach, since investment is not autonomous from cur- rent income, we can assume that consumption is split into an induced component and an autonomous component such that:3 a Ct = c(1 − t)Yt + Ct + Et (5) a Where c is the marginal propensity to consume, t is the tax rate, Ct is worker’s autonomous consumption financed out of endogenous credit money and Et is cap- 3The notation of the model has been slightly modified from the original contribution for consis- tency of notation through out the paper. 5 italists’ autonomous consumption expenditure. Consequently we can sum all the autonomous expenditures which are neither financed by income nor affect the pro- duction capacity of the capitalist sector as: a Zt = Et + Ct + Gt (6) Where Gt is government expenditure. In this model, we must have investment It being determined by current income, such that: It = htYt; (7) _ with h = htγ(ut − un) Where ht is the marginal propensity to invest, which is determined by the adjustment _ of the rate of capacity utilization, ut, to its normal level, un: h = htγ(ut − un). We can then see that, in this model, the short run equilibrium output is determined by the autonomous component of demand, Zt, such that: Zt Yt = (8) s − ht _ with s = 1 − c(1 − t). This means that, under steady state, as ut = un, h =u _ = 0, the rate of growth is given by the rate of growth of the autonomous component of demand: ∗ g = gZ (9) W Pariboni (2016) then suggests we assume that workers’ consumption, Ct , has an induced part and a credit-finance part, Bt, which is autonomous from current income Π and that capitalists’ consumption, Ct , is entirely determined by current income. In 6 this model we have that: W Ct = cw[(1 − π)Yt − (r + φ)Dt] + Bt; Π C = cππYt; t (10) a Ct = Bt − cw(r + φ)Dt; a ) Yt = Yt[cw(1 − Π) + cΠΠ + ht] + Ct Where Dt is the stock of accumulated debt, r is the interest rate, φ is the percentage of the D that is paid off in each period. In this version of the supermultiplier a model Zt = Ct , in other words, the autonomous component of demand is household debt-financed consumption. It is also possible to show that, in this case, we have that g∗ = gCa , where gCa is the exogenously given rate of growth of debt-financed consumption.“[T]his result implies that, given enough time, demand and output will tend to evolve at the rate of growth of the autonomous components of demand; in this case, workers’ autonomous consumption." (Pariboni, 2016, p. 224) Finally, it is also important to mention the work of Brochier and Silva (2018), which suggests a stock flow consistent Supermultiplier model where non-capacity creating autonomous component of demand is households’ consumption out of wealth.