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Rishabh Kumar Thrift, stagnation and wealth distribution in a two class economy with applications to the United States March 2015 Working Paper 06/2015 Department of Economics The New School for Social Research The views expressed herein are those of the author(s) and do not necessarily reflect the views of the New School for Social Research. © 2015 by Rishabh Kumar. All rights reserved. Short sections of text may be quoted without explicit permission provided that full credit is given to the source. Wealth accumulation and aggregate demand stagnation in a two class economy with applications to the United States Rishabh Kumar∗† July 13, 2015 Abstract A two class (capitalists and workers) model of economic growth is used to study long run stagnation of aggregate demand. Savings are differentiated by class and instead of a neoclassical production function, growth is demand driven. In our theoretical framework, capitalists can accumulate a higher share of wealth on the balanced growth path while simultaneously reducing the measure of aggregate demand for the entire economy. Applied to trends over 1979-2010, we find the US economy to represent the kind of stylized economy which would be prone to falling output capital ratios due to increased savings rate differentials in its income and wealth ranking. A first approximation suggests that the paradox of thrift maybe applicable to the decline in the share of savings of the US labor class. JEL Classification: D3, E21, O4 Keywords: Economic growth, Stagnation, Distribution, Paradox of thrift ∗ Department of Economics, New School for Social Research, New York I’m grateful to Duncan Foley for invaluable guidance and criticism throughout the development of this project. Comments, discussion and suggestions from Lance Taylor, Mark Setterfield, Paulo Dos Santos, Siavash Radpour and Anthony Bonen proved extremely useful. A working paper version of this paper is included in the bibliography. † 1 Introduction Does the concentration of wealth depress aggregate demand in the long run? In this paper we study such an issue in a two class (capitalists and workers) framework. Our theoretical findings are based on a demand driven approach to economic growth, rather than using a neoclassical production function technology. This methodology is able to relate two themes of recent interest - overaccumulation and unevenness in the distribution of wealth as a cause of chronic insufficiency of aggregate demand. We assign the inability of a growing economy to generate adequate demand under the moniker of secular stagnation. An inefficient equilibrium arises in neoclassical economies as a result of the technical coefficients of a production function rather than any long run feedback from spending behavior.1 These models were developed to highlight the stylized facts of a bygone era.2 New stylized facts have emerged in the industrialized world. As it stands, these facts are most relevant for the US economy, in particular an ever rising wealth income ratio, the concentration of capital income within a small segment of the population and the stagnation of wage income in real terms. An associated puzzle is the class aspect of savings. It is well established in the National Income and Product Accounts of the United States that the rate of saving as a percentage of GDP has been declining for the last three decades. How do we reconcile wealth accumulation and rising wealth-income ratios in the face of such facts? One simple explanation is that even for a fixed saving rate, the wage earning class has seen a falling share of income while the profit earning class has generated savings for both lifecycle and bequest purposes. Thus the income weighted saving rate is likely, in such circumstances, to go down for any class that undergoes income suppression. Depending on whether the class that loses its share in national income is the dominant contributor to consumption demand, the economy can end up with 1 Since the objective is to maximize consumption, the determinant of efficiency on the balanced growth growth path arises without any role for aggregate demand. 2 See Stiglitz (1969) for a summary and Saez and Zucman (2014) for empirical trends derived from the capitalization technique. Michl and Foley (2004) have demonstrated the breakdown of Okun’s law which relates output growth and employment. 2 higher wealth concentration ratios but lower rates of capacity utilization, as measured by the output capital ratio. In our model the primary vehicle for wealth accumulation by any class is their saving rate out of income. Classes are distinguished by the functional income distribution - one class earns wages and another earns profits - though both engage in savings. Aggregate demand stalls under a snowballing effect, which itself is driven by wealth accumulation. Since there are returns to wealth, higher savings can lead to more wealth and hence higher volumes of returns in the form of capital income. However increased savings depress the multiplier effect and lead to an aggregate paradox of thrift. As a simple behavioral exercise we assume that the rate of savings for any member of society is given but differentiated by class. This paper contributes by demonstrating underconsumption paths as a result of excessive savings, in a differential class savings model of economic growth. We derive an equilibrium where the rate of capacity utilization the Keynesian aggregate demand barometer - reacts negatively to the rate of savings by a capitalist class. Since the fictional economy of the model is a one good system, this implies a high equilibrium wealth income ratio as well as higher concentration of wealth. Full employment is not assumed, hence the capital labor ratio increases as capitalists engage in higher saving. The differential rate of saving is an economic force that can equalize or disequalize the distribution of wealth. If the two classes do not have substantially different rates of saving then in the limit, all wealth is distributed evenly and the corresponding rate of utilization is higher. We also show the possibility of one class completely dominating wealth, by saving enough and the economy ends up with the lowest possible rate of utilization - the floor for aggregate demand stagnation. We then investigate some empirical aspects of this paradox of thrift model by identifying these classes in the United States over the period 1979-2010. Calibrated to these data, the structural parameters of our model fulfill the stagnationist criteria. We conclude that the associated empirical trends - concentration of wealth and income and the declining income - wealth ratio is a result of capitalist oversaving and a long run aggregate paradox of thrift. 3 2 A growth model We will assume a closed economy and no government for the purposes of simple exposition. Two classes exist simultaneously, differentiated by their source of income - workers earn wages by selling their labor and capitalists/rentiers that own capital (means of production) which earns them a rate of profit (r). A single good is produced and can be consumed or accumulated as wealth, so that the terms capital and wealth can be used interchangeably.3 The feature of structuralist models of economic growth4 is that they permit an independence between the rate of accumulation (g, ie the investmentcapital ratio) and the volume of savings. Assuming a linear function to relate the rate of profit to the rate of capital accumulation, with the sensitivity = α > 0, gives us: coefficient ∂g ∂r g = g0 + αr (1) Where g0 is an accumulation component independent of the rate of profit. Note that the rate of profit (r) is simply the ratio of total profits to total capital (K). If the share of profits in output (X) is π the rate of profit can be decomposed in terms of the output capital ratio: r=π 2.1 X = πu K (2) Kaldorian savings with Pasinetti conjecture Aggregate Savings (S) is the sum of individual savings. We will assume Kaldorian savings propensities5 ie workers and capitalists have saving propensities sw and sc respectively with sc > sw under the presumption that workers engage in lifecycle saving only while capitalists can have a range of preferences over saving - bequest, retirement, wealth in the utility function and so on. It will turn out that the presumption sc > sw is crucial though easily explained. Firstly as Dynan et al. (2004) and Saez and Zucman (2014) find, 3 The cyclical nature of capital gains is suppressed for simplicity. The evidence in ? implies a more dominant role attributable to savings than capital price effects (72-28 volume v/s price ratio on average for the US) 4 See Taylor (2009) for a comprehensive exposition 5 Kaldor (1955) 4 the rate of saving goes up on the income and wealth ranking and it is natural to assume that capitalists are wealthier than workers given the former do not require selling their labor for income in the first place. The second point is that if sw is positive, then following Pasinetti (1962) we know that workers are also accumulating wealth6 which forms an additional source of income for them. Capitalists, therefore must save more than workers since they do not have similar dual income sources (wages and returns on wealth). Assuming a uniform rate of profit, savings can be decomposed into worker savings (Sw ) and capitalist savings (Sc ). S = Sw + Sc = sw ((1 − π)X + rKw ) + sc rKc In the above expression, sw is the average propensity of worker saving and sc is the average propensity of capitalist saving. Total wealth is decomposed into the wealth of workers (Kw ) and capitalist wealth (Kc ). With Z being the ratio of capitalist wealth to total wealth, by dividing the above expression by income X, we get the aggregate saving rate (s) for the economy weighted by the income and wealth share of the two classes. s= sc Zπ | {z } capitalist saving rate 2.2 + sw (1 − Z)π + sw (1 − π) | {z } (3) worker saving rate Reduced form expressions From the Investment-Saving identity (I ≡ S → gK = sX), we can solve (1), (2) and (3) to get the reduced form expression for the output-capital ratio7 (u) in terms of the functional income distribution (π) and the wealth ratio (Z): g0 u= = u(π, Z) (4) Zπ (sc − sw ) − απ + sw The expression above gives the instantaneous or short run output-capital ratio for given values of the distribution of π and Z. 6 The term Pasinetti conjecture is meant to signify his observation of Kaldor’s logical slip in presuming all wealth is owned by capitalists despite sw > 0 7 This represents the rate of capacity utilization of an economy without necessitating its dependence on a flexible production function technology. As a measure of aggregate X demand, it is the ratio of injection to leakages since u = K = gs 5 2.3 Long run We can now extend the short run analysis into a larger time frame. Long run behavior can be computed using growth rates for the aggregate economy and the distribution of wealth. Since g is defined as the gross accumulation = κ) can be described rate, the law of motion for capital stock per person ( K N as the following: κ̇ = κ(g − δ − γ) Where δ is the rate of depreciation of capital stock and γ is the rate of growth of population (N ). We take these rates as given and accommodate them under the natural rate of growth (n = δ + γ). Therefore the rate of growth of capital stock can be expressed as: κ̇ =g−n κ (5) The evolution of Z = KKc can be described using the growth rate of capitalist wealth vs the growth of total wealth in the economy.8 There is no class discrimination effect - both classes share the same reproduction rate and any wealth they lend as capital depreciates equally.9 Since capitalist wealth grows according to their rate of saving times the rate of return, we accordingly have the simple expression: Ẑ = K̂c − K̂ Ż = sc r − su = sc πu − su (6) Z Similar expressions for Z can be found in Samuelson and Modigliani (1966), Stiglitz (1969) and Michl and Foley (2004). However, the identity in (6) is distinguished by the fact that capacity utilization is not fixed in the long run and is neither a technical specification, thereby excluding the possibility of forced saving. Full utilization of available labor is therefore not guaranteed. ∴ 8 In this case, the change in wealth is the change in capital stock as permitted by available savings, since investment is driven independently of the volume of savings. 9 For the sake of analytical simplicity and long run analysis, we repress the cyclical effect of capital gains. 6 2.3.1 Labor Market An inverse relationship between the share of profits (π) and the rate of employment (λ = NL ) forms a convenient closure to our model, ie π = φ(λ), φ0 < 0 lim φ(λ) = +∞ λ→0 For analytical simplification, we do not consider movements in the average product of labor ( X = ξ) and take its level as given. Simple manipulation10 L of the above relationship yields the simpler form: π = φ(κ, Z) (7) The assumptions on the form of φ are not incompatible with neoclassical distribution theory, 11 reflecting its simplicity. We can now proceed to equilibrium analysis of this differential savings model of growth and distribution. 2.4 Equilibrium We want to analyze the impact of savings behavior by capitalists and workers, as it pertains to the long run equilibrium. From (4), (5), (6) and (7), a canonical form of the long run system can be written: u = u(π,Z) π = π(u,κ,Z) κ̇ = κ(κ,Z,π) Ż = Z(κ,Z,π) 10 The employment rate is the ratio of the labor force (L) and the population (N), λ= L X K u.κ . . = X K N ξ βξ As an example, consider the case where π = βλ = uκ where β is a parameter. Since ξ r = πu, this expression gives us r = β κ . The inverse relationship between r and κ under given levels of productivity ξ indicates similarity to the neoclassical assumption of diminishing marginal returns or r = f (κ), with f 0 < 0 11 7 At κ̇ = 0 and Ż = 0, the above expressions can be solved to get the equilibrium values (κ∗ , Z ∗ , π ∗ , u∗ ) in terms of the parameters sw , sc , α, g0 and n. (n − g0 ) sw − n.απ ∗ (8) π ∗ (g0 − n) (sc − sw ) αsw κ∗ = ξ. ∗ φ−1 (π ∗ ) (9) Z (g0 − n) (sc − sw ) + αn The value of π ∗ calculated12 from these expressions. The existence of positive equilibrium values rely on two simple parametric restrictions (besides real and positive values of the parameters): Z∗ = • n > g0 i.e. the natural rate of growth exceeds capital accumulation independent of the profit rate. Since at equilibrium, g ∗ = g0 +απ ∗ u∗ = n therefore the equilibrium rate of profit r∗ = π ∗ u∗ is positive when the natural rate of growth is greater than the exogenous accumulation rate. • sc > sw , which is the core of differential saving in this model. In the converse case, capitalist’s would have to go into debt to workers to finance their consumption. The equilibrium for the aggregate economy (κ∗ ) is stable13 when φ0 < 0 which follows from (7). 2.4.1 Equilibrium capital labor ratio, c∗ We do not assume full employment (else λ = 1). Thus we must distinguish between the capital stock per person (κ) and the capital labor ratio (c). The equilibrium capital labor ratio (c∗ ) is the ratio of the aggregate capital stock and the labor force (determined via the equilibrium rate of employment) and its expression is simply (9) divided by φ−1 (π ∗ ), viz: αsw (10) c∗ = ξ. ∗ Z (g0 − n) (sc − sw ) + αn The restrictions defined for (9) apply, thus c∗ is positively related to Z ∗ . Its relationship to the interclass savings differential in the denominator (sc − sw ) is non linear since sw also appears in the numerator. 12 The parametric representations have been suppressed here for simplicity. It is straightforward to calculate (8) and (9)√to get the expression for the wealth distribution at equilibsw (g0 −n)(2sc −3sw )+ rium, Z ∗ = tive root. 13 The stabilizing condition: (g0 −n)s2w ((g0 −n)(4sc sw −4s2c +s2w )+4αn(sw −sc )) 2(g0 −n)sw (sc −sw ) ∂ κ̇ ∂κ ||κ=κ∗ <0 8 being the posi- Contrary to the results of the neoclassical model of growth and distribution14 in Stiglitz (1969), our expression for c∗ highlights an important feature (since both include Z ∗ ) - the aggregate economy at equilibrium is not independent of the distribution of wealth. 2.4.2 Equilibrium output capital ratio, u∗ The expression for the rate of utilization or the output-capital ratio, u∗ can be computed at κ = κ∗ , Z = Z ∗ , π = π ∗ using the reduced form expression (4), viz: Z ∗ (g0 − n) (sc − sw ) + αn ∗ u = (11) αsw Since we have specified n > g0 , this implies that u∗ is inversely related to equilibrium wealth concentration - High shares of capitalist wealth should be associated with a lower average product of capital. We use u∗ and c∗ to study aggregate demand stagnation in a moment. 2.5 Stagnation in aggregate demand The usual supply side definition of economic stagnation is associated with low rates of the natural growth rate of the economy. In our case, this corresponds to the parameter n taking on low values. The recent decline of US economic growth argument associated with Gordon (2012) is reflective of such likelihoods. The demand side argument however, posits stagnation as a fall in the long run state of aggregate demand, through low utilization of capital at equilibrium. Thus even if high exogenous rates of natural growth (n) are associated primarily with growth of capitalist income, then given their high rate of saving, aggregate demand is stagnantionist. Without adequate demand, lower employment is generated per unit of capital (the equilibrium capital labor ratio should be high). The model presented in this paper can illustrate these features clearly, by taking the total derivative of u∗ and c∗ against capitalist 14 Stigtliz’ model uses linear savings-income behavior and shows the aggregate wealth at equilibrium is independent of equilibrium in the wealth distribution, although the converse is not true. 9 saving. For example: (−) du∗ = dsc dZ dsc (+) (−) z }| { z }| { z }| { (g0 − n) (sc − sw ) +Z ∗ (g0 − n) αsw (12) With the restrictions imposed (g0 < n, sc > sw ) earlier, (12) implies that economic forces that enable wealth concentration simultaneously constrain aggregate demand. If the total response of capitalist wealth concentration is positive to capitalist saving, then the term in the numerator is negative. Further, higher equilibrium values of Z ∗ will generate strong negative responses of utilization to the rate of capitalist saving (the right hand expression in the numerator). Taking the total derivative of (10) wrt sc , the second condition for stagnation - higher equilibrium capital labor ratios associated with higher capitalist savings is demonstrable. (+) (+) z }| { z }| { dZ αsw (n − g0 ) ds (sc − sw ) +Z ∗ ξ c ∗ dc = (13) dsc (Z ∗ (g0 − n) (sc − sw ) + αn)2 The numerator is positive under the parametric conditions and higher for dZ ) and stronger response of wealth concentration to savings propensity( ds c ∗ higher values of Z As a behavioral parameter, the saving propensity of the capitalist class is a crucial economic force in this model. The purpose of this section has been to show that its effect on aggregate demand and employment, through its distributional effect, is stagnationist. 2.6 Distributional regimes With the stagnationist effect arising from the economic forces of wealth concentration, the other role of capitalist saving is its impact on the distribution of wealth at equilibrium. We now study how even or uneven the resulting ownership of wealth may be, given capitalist preferences for wealth accumulation. 10 As a first step, it is informative to estimate the personal income shares of capitalists and workers from the functional income distribution (π ∗ ) at equilibrium. Since capitalists income only through their share of wealth, for any π = π ∗ , Z = Z ∗ the share of capitalist income (yc ) is: yc∗ = π ∗ Z ∗ 2.6.1 (14) Egalitarian wealth distribution For the sake of simplicity assume that out of the total population in the economy, a proportion (a) comprises rentiers. Thus, an even social distribution of wealth would be one where the equilibrium share of rentier wealth Z ∗ is equal to their proportion in total population, ie Z ∗ = a. Solving for sc at this value: (a − 2)(a − 1)(g0 − n)sw − n.α (15) sc = (2 + (a − 2)a)(g0 − n) • Corollary 1: If at equilibrium, both classes (workers and rentiers) exist then a simultaneous egalitarian equilibrium in wealth and income is impossible If the distribution of wealth is egalitarian then Z ∗ = a. In such a situation if income is distributed equally amongst all participants of society, then the share of rentier income is yc∗ = a. From (14) we know that this implies a = π ∗ Z ∗ . Since Z ∗ = a therefore this means a = aπ ∗ which is only possible if π = 1 that is all income is profits and hence every member of society is a rentier. 2.6.2 Workers own all wealth: Samuelson Modigliani regime Following Pasinetti (1962), a dual equilibrium was introduced by Samuelson and Modigliani (1966). The point of the latter exercise was to show the impacts of thriftiness on the part of workers - were their savings propensity to rise substantially, at equilibrium rentiers would be wiped out. Our model is also capable of generating such a result (ie Z ∗ = 0), ie all wealth at equilibrium belongs to workers. Naturally, with only wealth as a source of income, rentiers must be thriftier than workers. The following expression computes (solving for sc where Z ∗ = 0) the inter class savings rate differential, where rentier wealth is wiped out. If the differential (ψ = sc −sw ) 11 expands by any > 0, rentier wealth re-appears at equilibrium. The critical savings differential, necessary for a one class economy is: ψc = sc − sw = α n . (n − g0 ) 2 (16) • Corollary 2: At equilibrium, the share of rentier wealth (Z ∗ ) is greater than their share of income (yc ) and the two shares are equal only when rentier’s own no wealth. Since 0 < π ∗ < 1 by definition, the share of rentier’s income (yc = πZ) must be less than their share of wealth (Z). If rentiers have no wealth at equilibrium, so that Z ∗ = 0 then their share of income also falls to zero. This follows from the assumption that rentiers only earn income through returns on their wealth. 2.6.3 Rentiers own all wealth and lower bounds for utilization Can over-saving by rentiers drive Z ∗ to unity? This possibility has previously been taken up in models most famously by Pasinetti (1962) and Darity (1981).15 Since excess demand is set to zero by the Investment-Saving identity, we know that: Saving K̇ I |{z} z}|{ − K̇ S = 0 or κ̇I − κ̇S = 0 Investment Therefore from (1) and (3) we get g0 + απu − (sw + sc Zπ − sw Zπ)u = 0 Now at equilibrium g ∗ = sc π ∗ u∗ = n. Further by setting r = πu, we get: sc r∗ Z ∗ = r∗ (sc + sw Z ∗ ) − sw u∗ In Pasinetti’s case, a full employment-forced saving equilibrium dictated r∗ = snc which was later undermined by Samuelson-Modigliani’s Dual equilibrium where rentiers disappear completely. Darity showed an Anti-Dual equilibrium was also possible where the equilibrium value of Z can be greater than unity. In the case where local stability conditions of the aggregate economy are fulfilled, there would be an ever-increasing concentration of wealth. Z would tend towards but never reach unity. 15 12 Note that the above expression is still an identity and must be true in all cases. The scenario Z ∗ = 1 is only consistent with the unique case: u∗ = r∗ implying the utilization rate is equal to the rate of profit at equilibrium. • Corollary 3: If wealth is owned only by rentiers then the rate of profit and the rate of utilization at equilibrium are equal and workers are wiped out from the wealth and income distribution. This sets the limit to rentier saving sc If at equilibrium r∗ = u∗ then from r = πu it must be that π ∗ = 1. This implies all income comprises profits and is entirely wealth formation by rentiers (Z ∗ = 1). The unique saving rate that corresponds to this level is sc = rn∗ . This serves as the upper limit to rentier saving since beyond this value (sc > rn∗ ) excess demand (κ̇I − κ̇S ) does not correspond to zero at equilibrium. This extreme case also gives us a lower limit to the utilization rate where one class is entirely wiped out and we are left with a one class accumulation economy with strange properties.16 By definition, the share of rentier wealth can never be greater than one. 17 Endless wealth accumulation by a single wealth owning class is also explored in Piketty and Zucman (2014) where the wealth-income ratio 18 is the ratio of aggregate saving propensity to growth. As growth approaches zero, wealth grows unboundedly relative to income. These limits to the mathematical properties of our model and Piketty’s neoclassical model indicate that such low probabilities are not well defined in models of economic growth and remain the topic of conjecture. The point of this exercise has been to assimilate first approximations to wealth accumulating behavior primarily through the saving rate. That limits to aggregate demand are so intricately related to the complete concentration of wealth presents an important but less studied feature of growth and distribution. 16 A transcritical bifurcation on the parameter sc , appears as a source of an anti dual equilibrium in Taylor (2014). 17 Unless interclass borrowing is allowed, which would mean at equilibrium workers go into debt to sustain the capital labor ratio. One such possibility in a two class economy appears in Stiglitz (1969). Although in his case, classes are separated by an efficiency level which implies an interclass wage differential, rather than differences in the ownership of the means of production. 18 The inverse of the utilization rate in a one good model of accumulation 13 3 Wealth accumulation and stagnation in the US Economy? 1979-2010 Suppose we were to use the US economy as a numerical example for the model developed in the previous section. New savings have been shown to be responsible for 72 percent of wealth accumulation (the remainder being asset price recoveries)19 in the United States since 1970, despite a falling personal saving rate in the National Income and Production Accounts data of the Bureau of Economic Analysis. Translating the stylized fiction of our framework is relatively straightforward to actual economies - we use the wealthiest 1% of households as the patient capitalist class and the remaining households comprising wage earning workers.20 The period of analysis (19792010) is chosen, in keeping with the detailed income decomposition made available by the Congressional Budget Office (CBO).21 In the data of Saez and Zucman (2014), wealth concentration as a phenomena begins to emerge during the same period. A simple numerical calibration brings out the relationship between aggregate demand stagnation and wealth concentration. We use sc = 0.4 as an approximation of capitalist saving rates (based on Saez and Zucman’s data) and sw = 0.05 as the worker saving rate (NIPA personal saving rate) and fix one and vary the other to illustrate the effects of class savings behavior. With a long run compounded annual growth rate of 2.6 percent, the remaining parameters are simply chosen to fulfill the feasibility condition (n > g0 ) and congruent with a five percent net rate of profit.22 The table below summarizes the total derivatives of utilization and wealth concentration against the capitalist saving rate. Both responses correspond to the stagnation conditions ie equilibrium demand falls and wealth concentration responds positively. At a 28 percent saving rate, capitalists would 19 See Piketty and Zucman (2014) This terminology is common in the contemporary literature owing to capital income and wealth concentration within the top 1 percent of US households - see for example Taylor (2014), Stiglitz (2015a), Stiglitz (2015b) and Mankiw (2015). 21 Distribution of Household Income and Federal Taxes: 2010, CBO 22 The average rate of return over our chosen period at three percent depreciation. Source: Piketty and Zucman (2014) 20 14 disappear in the long run and at about 30 percent, the distribution of wealth would be proportional with the class share of population. Response dZ ∗ /dsc du∗ /dsc Numerical Value 4.08623 (-)4.72089 Table 1: Full responses of Z and u to sc at equilibrium, calibrated at sc = 0.4, sw = 0.05, g0 = 0.01, α = 0.28, n = 0.025. Since the response of u∗ (Z ∗ ) is negative (positive), the stagnation criteria is fulfilled at these values Now suppose we were to fix the worker saving rate and increase capitalist saving propensity, what associated equilibrium would emerge in utilization and distribution - and how does this compare to doing the opposite? In the figure below, the left panel fixes sw = 0.05. Note that as sc rises, it bring down capacity utilization (u∗ ) but simultaneously increases both the dyc∗ dZ ∗ ∗ ∗ share of capitalist wealth (Z ) and income (yc ) with dsc > dsc . For the given parameters, responses of capitalist wealth and income are unbounded beyond sc = 0.48, ie they reach the limit where u∗ = r∗ . If capitalist saving rates are sufficiently low, they go into debt to workers (Z ∗ < 0) in order to finance their consumption. yc * Z* u* yc * Z* u* 1.2 1.0 0.5 0.8 0.2 0.3 0.4 0.5 0.6 0.7 0.8 sc 0.6 0.4 -0.5 0.2 -1.0 0.02 0.04 0.06 0.08 0.10 sw Figure 1: Simulations holding sw (left) and sc (right) fixed. Calibrated at sc = 0.4, sw = 0.05, g0 = 0.01, α = 0.28, n = 0.025 On the other hand, increasing worker saving reduces capitalist wealth 15 and income concentration.23 But given that sc > sw , worker consumption is a critical driver of aggregate demand thus dragging it down at a faster rate than in the capitalist saving experiment. As sw approaches zero, the economy moves toward overutilization (u∗ > 1) with consumption driven up high enough to outpace capacity. To identify which of the two structural parameters (sc or sw ) has changed in the actual economy, the comparative trends can help establish plausible explanations. If aggregate demand and wealth concentration24 both decline then it is likely that oversaving is attributable to workers. Conversely if wealth concentration increases and aggregate demand declines then capitalist wealth accumulation is a likely cause for unutilized productive capacity and the average product of capital is low. The paradox of thrift applies in both cases. Discussion 40 Income−Wealth Top 1 Wealth Share Top 1 Income Share 25 Percent 30 35 10 12 8 6 15 4 10 2 0 saving propensity ratio Top 1 saving rate vs economy 20 4 1980 1985 1990 1995 2000 2005 1980 Year 1985 1990 1995 2000 2005 2010 Year Figure 2: Left Panel: Ratio of top 1 saving rate vs total saving rate. Right panel: National income-private wealth ratio, Share of wealth and income of top 1 percent. Source: Piketty and Zucman (2014) and Saez and Zucman (2014) 23 Worker saving being for lifecycle reasons, is simulated for a small range [0, 0.1] to illustrate its impact 24 We use the term concentration under the assumption that the economy is predominantly workers with a small fraction (such as the richest one percent we use) being wealthy capitalists 16 If we consider the corresponding US empirical trends over 1979-2010, the implications of our model become clearer. The savings rate of the top one percent has consistently and increasingly dominated the national saving rate, going up to as much as ten times between 1995 and 2005.25 The composite pattern was made up of a stable savings rate at the top of the wealth distribution while much of the bottom of the distribution saw a declining saving rate. The right panel in the above figure shows the actual trends (which are also likely to be associated with capitalist oversaving in our model) - the income to private wealth ratio26 has been falling consistently while the share of wealth and income became more concentrated. Observe that the concentration of wealth (top 1 percent wealth share) has exceeded income-private wealth ratio consistently since 1990. Empirical counterparts are translated into capitalists and workers, so this corresponds to: X Kc > K K then, Kc > X If If the stock of capitalist wealth exceeds national income by a significant margin, then the stagnationist effect is significant even in the short run. Suppose Kc = 2X and the rate of profit r is 5 percent. In the next period thus, capitalists earn as income rKc = 0.1X. With the 1-99 class distribution, 10 percent then gets divided amongst one percent of the population while the remaining workers get 90 percent. If the working class consumes everything and the capitalist class consumes 40 percent then only 96 percent of the income forms consumption demand. The leakage from the spending multiplier contributes to more wealth formation and wealth becomes even more concentrated as the effect snowballs into the long run. To complete the puzzle of new savings turning into wealth - with a stable wealthy saving rate and declining savings for the rest of the economy - it suffices to elaborate the changes associated with income at the margin. For a 25 The period 2005-2010 is suppressed since the personal savings rate was negative over much of this period 26 Without a production function this serves as a proxy for the output capital ratio in the one good closed economy model of accumulation 17 given level of long run autonomous consumption, it is plausible that the top one percent have a (close to) zero marginal propensity to consume. Once these given consumption requirements are met, income growth within this class does not significantly contribute to consumption demand. In the table below, note that every component of income27 for the Top 1% grows faster than NIPA consumption expenditure, while for the remaining households even income supplemented with transfers is unable to match the growth in consumption. Thus over the long run, the 1-99 income distribution can generate demand only through intervening income supplements so that any deficit spending contributes to consumption rather than building long run productive assets. Measure Income Wages Rental Income Capital Income Top 1% 1.526 1.522 1.748 1.093 Bottom 99% -0.4 -0.9 -1.095 -0.948 Table 2: CAGR of class specific incomes components less CAGR of household consumption expenditure (1979-2010) With these theoretical and empirical conclusions, it would be reasonable to categorize the industrially mature US economy of recent decades as one prone to (and likely undergoing) a phase of aggregate demand stagnation due to an inherent class character. There are related and contributing factors to stagnation from the supply side as well28 but beyond the scope of our exposition. The stress and chronic insufficiency of aggregate demand comes out as a consequence of wealth accumulation, a feature which is not easily explained by the neoclassical theory of distribution. 27 This data uses the CBO’s income ranking instead of the wealth ranking. 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