The limits to profit-wage redistribution: Endogenous regime shifts in Kaleckian models of growth and distribution

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1 Institute for International Political Economy Berlin Te limits to profit-wage redistribution: Endogenous regime sifts in Kaleckian models of growt and distribution Autor: Kasper Köler Working Paper, No. 112/2018 Editors: Sigrid Betzelt, Eckard Hein (lead editor), Martina Metzger, Jennifer Pedussel Wu, Martina Sproll, Cristina Teipen, Acim Truger, Markus Wissen, Reingard Zimmer

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3 Te limits to profit-wage redistribution: Endogenous regime sifts in Kaleckian models of growt and distribution Kasper Köler Abstract A feature of Kaleckian models of distribution and growt tat is often overlooked is tat tey describe a nonlinear relation between functional income distribution and demand and growt, because te size of te multiplier is affected by redistribution from wages to profits and vice versa. Tis paper addresses te nonlinearity of te standard post-kaleckian model by examining its so-called IS-curves. It is found tat canges in functional income distribution affect te distribution-ledness of an economy: redistribution towards wages reinforces te wage-led or profit-led caracter of an economy, wile redistribution towards profits does te opposite. In addition, redistribution towards wages can turn an intermediate regime wage-led. A standard post-kaleckian model wit nonlinear investment beaviour is ten presented. Tis model yields substantially different IS curves, suc tat an optimal functional income distribution can be derived. However, it is found tat unlike in te standard model, tis optimum is not te same for te different classes, suc tat true opposing interests appear in te model. JEL classification: B59, E11, E12, E25, O40 Keywords: Distribution, growt, nonlinearity, demand and growt regimes, Kaleckian models Contact: kasperkoler@gmail.com Acknowledgements: I would like to tank Eckard Hein and Marc Lavoie, for teir guidance, and Ryan Woodgate and Franz Prante for elpful comments. All remaining errors are my own.

4 1. Introduction Te well-known post-kaleckian growt model, developed independently by Baduri and Marglin (1990) and Kurz (1991), and based on earlier models by Rowtorn (1981), Dutt (1984) and Taylor (1985), is now commonly used for questions about growt and distribution in post-keynesian analysis (Hein, 2017; Lavoie, 2014, Capter 6). Te merit of tis model and its extensions is tat tey address long-run growt and capacity utilisation, wile incorporating functional income distribution. As a result, a large branc of eterodox economic literature is concerned wit te distinction between wage-led and profit-led demand and growt regimes, te former referring to a situation in wic an increasing profit sare in national income leads to a slowdown in capital accumulation and declining capacity utilisation, wile te opposite olds for te latter. Tis distinction as in particular been te basis of a substantial amount of empirical researc, often centred around te question of weter demand and growt are profit-led or wage-led 1. However, te interpretation of demand and growt regimes as static constellations is problematic, since tere is no reason to assume tat regimes do not cange over time. Moreover, most of te literature on te post-kaleckian model as so far ignored te question of te sustainability of demand and growt regimes: does a profit-led regime remain profit-led after pursuing a profit-led growt strategy, i.e. after persistent income redistribution from wages towards profits? Te same question can be asked for te wage-led regime. In oter words: does te profit sare ave an upper (or lower) tresold at wic an economy switces from a profit-led growt regime to a wage-led regime and vice versa, and if so, wat factors determine tis tresold? Tis is te central question tat will be addressed in tis paper. Te opacity surrounding wat exactly determines te demand and growt regime an economy is in and wen suc regimes cange as fuelled a number of critiques. Of course, wit given investment and saving functions, it is possible to analytically derive te required conditions for te existence of certain regimes, as Hein (2014, p. 265) does. However, as Palley (2014b, p. 2) notes, te parameters tat determine weter tese conditions are fulfilled are usually seen as deep primitive parameters ; tey are regarded as exogenous and terefore seldom subject to furter examination. According to Palley, researcers sould be cautious wen basing teir policy advice on weter an economy seems to be wage-led or 1 See for example Onaran and Galanis (2013), Stockammer and Ederer (2008) and Stockammer, Onaran and Ederer (2008) 1

5 profit-led, because te currently prevailing regime can be te result of existing policies and institutions, rater tan being fixed and natural. Suc institutional and political factors ave been igligted especially by Palley (2012; 2013a; 2013b; 2014; 2016), but also by Carvalo and Rezai (2015), Nikiforos (2016) and Prante (2017). Blecker (2016) puts forward a different critique of te empirical studies. He argues tat profits are cas flows and affect current investment as suc, wile aving no effect on te desired capital stock and, terefore, on long run investment. Te sensitivity of consumption to canges in income, on te oter and, is small in te sort run, but stronger in te long run, as Blecker points out. Te reason for tis is tat ouseolds tend to respond to incidental canges in income by increasing or decreasing teir saving, wile tey will cange teir consumption patterns in te face of permanent canges. Blecker argues tat economies are terefore more likely to be profit-led in te sort run tan in te long run; econometric results suggesting tat an economy is profit-led can terefore be misleading. A tird strand of Kaleckian literature is dedicated to te possibility of nonlinear relations witin te post-kaleckian model. Again, suc nonlinearities can complicate or even invalidate empirical researc. In particular, nonlinearities ave te potential of making demand and growt regimes endogenous, in te sense tat te regime depends on functional income distribution. A tresold as described above ten appears, so tat redistribution towards wages or profits can cause a regime to sift wen tat tresold is reaced. Tis poses a limit to te virtuous process described by Stockammer (2011), in wic redistribution towards profits in a profit-led regime or towards wages in a wage-led regime induces ig growt. Indeed, it is clear tat te profit sare cannot rise to 100 per cent, nor fall to zero per cent: tese scenarios are simply irrelevant for a model tat seeks to capture te dynamics of growt and distribution in a capitalist economy, of wic bot profits and wages are an inerent component. However, tey do raise te question of wat te limits to profit-wage redistribution in a capitalist economy are, and of wat factors determine tese limits. Te aim of tis paper is terefore twofold: on te one and, it is to assess te teoretical potential for regime sifts in te post-kaleckian model. On te oter and, it is to analyse te effect of functional income distribution on distribution-ledness, i.e. te degree to wic an economy is wage-led or profit-led (Nikiforos, 2016). As a result, a considerable amount of 2

6 attention will be devoted to nonlinearities in te post-kaleckian model, bot systemic and beavioural. To keep te exposition clear and focussed, several contributions to and elements of te literature on wage-led and profit-led regimes will left out of te analysis. Firstly, tis applies to Blecker s (2016) distinction between sort run and long effects. Altoug is argument is certainly interesting, it does not concern regime sifts, strictly speaking. Secondly, tis paper will not join te debate on te normal rate of capacity utilisation and te susceptibility of te Kaleckian models to Harrodian instability, of wic Skott (2012) is peraps te most vocal exponent. Instead, te Kaleckian ypotesis tat te rate of utilisation is an adjusting variable in te long run will simply be assumed to old. Finally, te effect of capacity utilisation on functional income distribution will be disregarded. Altoug tere are powerful arguments for assuming tat tis effect matters, I would like to argue tat tere are numerous factors tat affect functional income distribution, many of tem political and institutional and terefore difficult to incorporate in economic models. Furtermore, disregarding tis feedback effect facilitates a clearer analysis of te effect of functional income distribution on demand and growt. It will terefore be assumed tat te profit sare is a completely exogenous variable, so tat te causality runs in only one direction. Te remainder of tis paper is structured as follows. Te next section outlines a simple version of te post-kaleckian model, and discusses te degree to wic distribution-ledness varies in tis model. Section 3 presents a critique of te post-kaleckian model, aimed at te sustainability of persistent wage-led and profit-led strategies, wit a focus on nonlinear beavioural equations. In Section 4, a simple post-kaleckian model wit a nonlinear accumulation function (based on suggestions by Nikiforos, 2016) will be presented and analysed. Section 5 provides a brief summary and some concluding comments. 2. Distribution-ledness and regime sifts in te standard model Te main result of te post-kaleckian model is tat growt and demand can be eiter wageled or profit-led. Te factors determining wat regime applies to an economy ave been discussed extensively in te Kaleckian literature. However, wile te model is designed for dynamic analysis, its results are usually interpreted as being static by nature; an economy is caracterised by eiter profit-led or wage-led growt, and eiter profit-led or wage-led capacity utilisation. Te way te IS curve in te profit sare capacity utilisation space was 3

7 originally depicted by Baduri and Marglin (1990) can be seen as a symptom of tis. Te IS curve sows all dynamic equilibria for a given set of values for te exogenous parameters, wile relating te profit sare to capacity utilisation. In oter words, it sows te effect of a cange in te profit sare on te equilibrium rate of capacity utilisation, keeping everyting else constant. For simplicity, Baduri and Marglin produce a linear IS curve, wic is upward sloping for te profit-led regime, and downward sloping in te wage-led case. Tis curve tus suggests tat a cange in functional income distribution as no effect on te extent to wic an economy is profit-led or wage-led. Few researcers seem to be interested in tis: altoug several autors (e.g. Blecker, 1989) present a nonlinear IS curve, te exact sape of te curve is seldom explicitly discussed. Tis is odd because, as will be demonstrated below, te IS curve is only linear in a very specific case. Furtermore, te fact tat te curve is nonlinear in all oter cases proves te relevance of te concept of distribution-ledness 2. Nikiforos (2016) presents a Kaleckian model in wic te degree of distribution-ledness canges endogenously; owever, te simple versions of te Kaleckian distribution and growt models already contain te possibility of canging distribution-ledness, and even albeit to a very limited extent te possibility of regime sifts, as a result of functional income redistribution. Te model used for te analysis in tis section is a simple post-kaleckian growt model, based on Hein (2014, Capters 6 & 7). It is set in a world of oligopolistic competition, suc tat firms ave te power to set prices witin certain limits. Tey do so by marking up unit labour costs:! = (1 + &) ( ), (2.1) were! is te price level, & te mark-up, ( te total wage bill and ) total output. Te mark-up is determined by te institutional caracteristics of te economy, suc as market concentration and trade union power (Hein, 2014, Capter 5). Functional income distribution is terefore regarded as a variable exogenous to te models, determined by te mark-up of firms: 2 Nikiforos (2016) proposes a matematical definition of distribution-ledness, but tat definition is somewat less applicable to te explicit model presented ere. Instead, te term will be used ere to refer to te degree to wic capacity utilisation and/or growt are wage-led or profit-led. In matematical terms, it tus simply refers to te slope of te IS curve. 4

8 =,!) =!) ( (1 + &)( ( =!) (1 + &)( = & 1 + &, (2.2) were is te profit sare in total income and, aggregate profits. Furtermore, it is assumed tat firms operate below full capacity output, so tat tey can produce more wen demand increases; an increase in demand as a quantity effect rater tan a price effect. Output is completely omogeneous, as are capital and labour. Te rate of profit. in tis economy can be decomposed as follows:. =,!/ =,!) ) ) ) / = 1 2, (2.3) were / stands for te (real) capital stock, ) for potential output (i.e. full capacity output), 1 for te rate of capacity utilisation and 2 for te capital-potential output ratio. Finally, tere are two beavioural equations, wic describe aggregate saving and aggregate investment; bot are normalised by te capital stock for convenience. Te saving rate 3 is often presented as a linear function of te profit sare and te rate of utilisation: 3 = 4!/ = 5 6. = , 0 < 5 6 1, (2.4a) were 4 stands for aggregate saving and 5 6 for te propensity to save out of profits. Tis function describes te most basic case in wic tere is no saving out of wages; only recipients of profit income are assumed to save. However, it can be easily adjusted to include saving out of wages (4 : ): 3 = :!/ = 5 6, + 5 : (),) = [5!/ : + (5 6 5 : )] 1 2, (2.4b) were 4 6 is saving out of profits and 5 : is te propensity to save out of wages. Altoug Baduri and Marglin (1990) present an implicit investment function, simply noting tat investment depends on te profit sare and te rate of capacity utilisation, I will use te explicit investment function proposed by Kurz (1991), since tis enables a more elaborate analysis of te demand and growt regimes. Tis explicit function also includes a constant =: In equilibrium, saving and investment must be equal: > =? / = = + A. (2.5) 5

9 > = 3, (2.6) so tat te equilibrium values for growt and capacity utilisation are: 1 = = + A [5 : + (5 6 5 : )] 1 (2.7) > = (= + A)[5 : + (5 6 5 : )] 1 2 [5 : + (5 6 5 : )] 1 (2.8) Under a classical saving assumption (i.e. 5 : = 0), tis simplifies to: 1 = = + A, 5 6 > = (= + A) (2.7a) (2.8a) For tese equilibria to be stable, a Keynesian stability condition must old: D3 D1 D> D1 > > 0. (2.9) Te first order derivatives wit respect to te profit sare of te equilibrium values can be bot positive and negative, so tat demand and growt can be bot wage-led and profit-led: D1 D = = 5 62 I, G D> D = GA I @A =@H I. G5 6 (2.7b) (2.8b) Since (2.7b) is always negative wen (2.8b) is, tere are tree possible regimes: te wage-led (or cooperative stagnationist, in te terminology of Baduri and Marglin) regime, te intermediate (or conflictual stagnationist) regime and te profit-led (or exilarationist) regime. Te intermediate regime is te special case in wic capacity utilisation is wage-led, 6

10 wile growt is profit-led. Te conditions for profit-led capacity utilisation and growt are, respectively: and D1 D > 0 = (2.7c) D> D > 0 AI > 2@A + =@. (2.8c) As noted by Baduri and Marglin (1990), te IS curve in te profit sare and capacity utilisation space ereinafter referred to as te utilisation curve can ave two basic sapes: it can appear bot as a rising and as a declining line. However, neiter of tese sapes are linear: te slope of bot lines is decreasing. In oter words, te wage-led or stagnationist regime becomes less wage-led wen te profit sare increases, wile te profit-led or exilarationist regime becomes less profit-led. Tis is sown below in Figure (a) (b) Figure 2.1: Utilisation curves of te post-kaleckian model, wage-led (a) and profit-led (b) Matematically, tis result is unsurprising: te profit sare only appears in te denominator of te first order derivative, so tat te denominator increases wen te profit sare increases and te slope terefore declines. Economically, te reason beind tese sapes is somewat less obvious, but logical upon closer inspection. A profit-led regime can arise wen a iger profit sare leads to a iger rate of capital accumulation by firms. Tis 7

11 can ave a strong positive effect on overall capacity utilisation in te economy, because te increased investment leads to increased employment, and te increased wages tat are paid lead to increased consumption expenditure. Tis is te process tat lies beind te Keynesian multiplier. However, a iger profit sare means a lower wage sare: every increase in employment (and terefore in investment) will terefore lead to lower consumption expenditure wen te profit sare is iger. Tis is sown by te simple Keynesian investment multiplier: as a iger profit sare by assumption leads to a iger average propensity to save, te multiplier K) = K?/5 decreases. Tis is also true in a dynamic context. Redistribution towards profits in te profit-led regime is terefore less effective wen te profit sare is iger, wile redistribution towards wages in te wage-led regime is also less effective; te Baduri-Marglin model tus suggests tat wage-led demand exibits increasing marginal returns, wereas profit-led demand suffers from te opposite 3. Te story becomes somewat more complicated, owever, wen one looks at growt and capital accumulation as well. As is well-known, te wage-led regime can be eiter cooperative or conflictual ; te former means a iger wage sare leads to iger growt and profit rates, wile te latter refers to te opposite (Baduri and Marglin, 1990). Te conflictive version of te wage-led regime, wic Baduri and Marglin connect to te Marxian profit squeeze teory, as been recognised as a separate tird regime by oters (e.g. Hein, 2014). Tis intermediate regime is caracterised by wage-led capacity utilisation, but profit-led growt. Te condition for a positive first order derivative of output growt wit respect to te profit sare is te same as tat of te profit rate: D> D > 0 AI @A =@ > 0, (2.8d) D. D > 0 AI @A =@ > 0. (2.3a) Since tis condition contains te profit sare itself, it is clear tat te level of te profit sare affects not only te degree of distribution-ledness, but also wic regime applies to an economy. In oter words, te caracter of te regime can cange wen functional income distribution canges, wic can be seen clearly from te IS curve in te profit sare- 3 A similar analysis is presented by Prante (2018). 8

12 accumulation space (Figure 2.2). In te remainder of tis paper, tis curve will be referred to as te growt curve. > > (a) (b) Figure 2.2: Growt curves of te post-kaleckian model, wage-led (a) and profit-led (b) Again, two different sapes are possible. Clearly, te sape of te curve does not depend on te sign of te first order derivative. Instead, te sign of te second order derivative determines te sape of te curve; a positive second order derivative means tat te slope of te curve is increasing, as in Figure 2.2a, wile te opposite means tat te growt curve of Figure 2.2b appears. Te condition for sape (a) is tus: D I > D I = 2@ 5 62 G@A + = H M > 0. G5 6 (2.8e) Since te stability condition requires tat te denominator is positive, tis can be simplified to: D I > D I > > = (2.8e*) Tis is te exact same condition as for te wage-led demand regime, wic is wy sape (a) in Figure 2.2 is labelled te wage-led sape, even toug it as bot an upwards sloping and a downwards sloping part. In contrast, sape (b), wic coincides wit te profit-led demand regime, is unambiguously profit-led. Tus, wile growt becomes more profit-led (or less wage-led) as te profit sare increases in te first case (Figure 2.2a), it stays more or 9

13 less consistently profit-led in te second case (Figure 2.2b). We can tus say tat wile redistribution towards profits becomes progressively less effective wen it comes to capacity utilisation, tis is not true for te growt and profit rates. How can tese sapes be explained? Clearly, te equilibrium growt rate is affected positively by te profit sare, wile te profit sare also as an indirect effect troug te rate of capacity utilisation. It is terefore not surprising tat profit-led capacity utilisation coincides wit profit-led growt and profit rates, since in tat case bot te direct and te indirect effect are positive. Neverteless, te exact sape of te profit-led growt curve in Figure 2.2b is not tat obvious; it seems to be almost vertical at first, to become a straigt upwards sloping line after bending somewat. As explained above, te profit-led utilisation curve flattens because of te lower average propensity to save tat results from an increasing profit sare. Since te rate of capacity utilisation is a relatively unimportant motivator for accumulation in te profit-led regime, te effect of a lower investment multiplier is not very strong in te profit-led growt curve in Figure 2.2b, so tat te slope is declining only slowly. Te first sape, in Figure 2.2a, can be traced back directly to te sape of te utilisation curve. Since te effect of functional income redistribution on equilibrium capacity utilisation diminises as te profit sare increases, troug te already discussed declining multiplier effect, tis in turn affects te equilibrium growt rate. As te indirect effect of te profit sare on te accumulation rate declines, te direct effect becomes more prominent, meaning tat after a certain tresold, te direct effect overtakes te indirect effect. Te value of tis tresold is determined by te propensity to save, te capital-potential output ratio and te investment coefficients. Tis seds some new ligt on te discussion by Baduri and Marglin (1990) on cooperative capitalism. Baduri and Marglin argue tat te critical analytical condition for te successful working of tis model of cooperative capitalism is tat te normalised value of total profit [ ] must decrease as te real wage rate decreases and te profit sare correspondingly increases (ibid., p. 382, empasis in te original). Wen tis condition is not fulfilled, tey argue, a situation of profit squeeze arises, tat is, wat is usually called te intermediate or conflictive regime. However, te analysis above clearly sows tat a wageled strategy in a wage-led regime will always succeed, as long as it is maintained for long enoug. Even wen growt and te profit rate respond in an adverse way at first, te 10

14 intermediate regime sifts to a full wage-led regime as soon as te profit sare falls below te tresold defined above (tat is, wen tere is no cange in te beavioural parameters). Te success of a wage-led strategy tus depends on te perseverance of policymakers. Completeness requires one last remark regarding te IS curves of te simple post- Kaleckian model, wic is tat a tird constellation can arise, besides te two combinations of capacity and growt curves described above. Tis is te situation in wic te first order derivative of te utilisation rate and te second order derivative of te growt rate wit respect to te profit sare are exactly equal to zero. Te condition for tis is: D1 D = DI > D I = = =5 6. (2.7d) In tis case, te growt curve is a straigt upwards sloping line troug te origin (wit a slope equal to A), wile te utilisation curve is a flat orizontal line. Capacity utilisation is tus unaffected by functional income redistribution in tis case, wile te growt and profit rate are strongly profit-led. Tis result simply means tat consumption and investment effects on effective demand cancel eac oter out completely, and te degree of distribution-ledness is completely constant. 3. Te case for endogenous regime sifts Te analysis in te previous section sows tat te standard post-kaleckian model is rater versatile. However, some questions about te sapes of te IS curves do remain. First of all, tere is no possible endogenous sift from wage-led to profit-led capacity utilisation and vice versa; tat is, canges in te profit sare alone cannot cause suc a sift. Secondly, it is unclear wat te limits to functional income distribution are: according to te model, wageled regimes remain wage-led, even wen te wage sare approaces 100%, wile profit-led regimes remain profit-led, even wen te wage sare is almost non-existent. Terefore, tis section presents alternatives to tis puzzling caracteristic of te model. To tis end, te (nonlinear) IS curve sapes proposed in te literature will be assessed first, after wic te relevance of nonlinear beavioural equations is discussed. 11

15 3.1 Oter proposed IS curve sapes Several autors ave suggested tat te utilisation curve may be nonlinear 4. Marglin and Baduri (1991, p. 145) extensively discuss te sape of tis curve, noting tat all discussion of te sape of te IS scedule is necessarily ypotetical. Te trut is tat we know relatively little about its sape even in te neigbourood in wic te economy as actually been operating and even less about its global sape. However, tey argue tat recent trends can indicate te approximate sape. Moreover, Marglin and Baduri offer some speculative ideas temselves, and provide two potential utilisation curve sapes, sown below in Figure (a) (b) Figure 3.1: Utilisation curve sapes, as suggested by Marglin and Baduri (1991) Tey also discuss te implications of tese sapes: in te case of sape (a), te economy is wage-led wen capacity utilisation is low, and profit-led wen it is ig. Sape (b) indicates tat te economy is wage-led for low levels of te profit sare, and profit-led for ig levels. Unfortunately, Marglin and Baduri provide no explanation as to wy tis would be te case; it is unclear wat te reason for te existence of suc dynamics would be, or in wat kind of situation tey would arise. Furtermore, even toug bot IS curves indicate tat a cange in functional income distribution can cause a regime sift, te main concern described in te introduction to tis section remains: wage-led economies stay wage-led even wen te 4 Autors in te social structure of accumulation (SSA) tradition ave also proposed nonlinear relations between profits, demand and growt (see for example Bowles and Boyer, 1988; Gordon, 1995). Tese auors are, like many Kaleckians, concerned wit te distinction between wage-led and profit-led growt, but take a more institutionalist/marxist, power-oriented approac. 12

16 wage sare approaces unity, wile profit-led economies can trive wit a negligible wage sare. Taylor (1990), You (1994) and Palley (2013b) all present wat is essentially te opposite of te curve in Figure 3.1b. Tis curve is sown below in Figure Figure 3.2: Te utilisation curve, according to Taylor (1990), You (1994) and Palley (2013b) In tis situation, te economy is wage-led for ig levels of te profit sare, and profit-led for low levels. Increasing te profit sare tus makes te economy less profit-led, wile increasing te wage sare does te opposite; bot wage-led and profit-led strategies ave decreasing marginal returns. Suc a utilisation curve does not ave te problems described above and tus makes some intuitive sense, but tat does not necessarily make it a more appropriate representation of reality. Te autors all provide a limited explanation of teir reasoning. You (1994, p. 217) simply refers to Marglin and Baduri (1991), noting tat te actual sape of te IS curve is unknown, and tat te displayed sape is cosen for illustrative purposes only. Taylor (1990, p. 333) refers to stronger profit effects on investment as te real wage rises, but does not substantiate tis assumption. Palley (2013b, p. 7) argues tat rising marginal costs of capital stock adjustment limit te rate at wic new capital can be added and absorbed into organizations and tat a cange in functional income distribution causes te saving rate to cange. Tis argument is of course already included in te standard post-kaleckian model, wic does not lead to te reversed U-sape in Figure 3.2, unless Palley is referring to nonlinear saving beaviour. 13

17 3.2 Nonlinear beaviour Te IS curves in Section 3 are based on te assumption tat te saving and investment functions are linear; relaxing tis assumption would lead to different outcomes. Altoug te assumption of linear beavioural equations is standard in te Kaleckian growt literature, some autors ave suggested tat nonlinear functions resemble reality more closely (see for example Nikiforos, 2016). Te idea of nonlinear beavioural equations is far from new; Robinson (1962) assumes tat accumulation is a nonlinear function of te rate of profit, altoug se provides no strict arguments for te nonlinearity. In an even earlier paper, Kaldor (1940) argues tat bot saving and investment are nonlinear functions of output. He notes tat firms are not likely to invest more wen capacity utilisation is low, even wen profits increase. Furtermore, wen capacity utilisation is at a very ig rate, firms attempting to accumulate at a iger speed will face increasing costs. Tis notion strongly resembles Palley s (2013b) argument mentioned above. However, contrary to Kaldor s (1940) investment function, te Kaleckian versions do explicitly include capacity utilisation and profits, so tat Kaldor s first argument is already included in te model 5. Moreover, it is doubtful weter firms will really slow down accumulation as a result of increasing costs wen capacity utilisation is very ig; te underlying mecanism leading to rising costs (i.e. scarcity driving prices up) sould also work for te output of te firms attempting to invest more, so tat investment still constitutes a profitable business opportunity. And, if tis not te case, ten tis means tat te profit sare is declining, wic as its own separate effect in te post-kaleckian investment function. Tere is also no clear reason wy te financing of investment would become more difficult wit a iger rate of capacity utilisation; if anyting, banks are more optimistic and likely to provide loans in te boom pase of te business cycle, as Minsky (1977) famously argued. Nikiforos (2016) provides a more elaborate explanation as to wy te beavioural equations would be nonlinear. He argues tat profits matter for investment decisions for two reasons: because current and recent profits are te best indication firms ave for future profitability and terefore for te success of teir investments, and because profits can be retained, wic is crucial for te financing of investment. According to Nikiforos, current 5 It could be argued tat tere sould also be an interaction variable, as Kaldor asserts tat te effect of profits on investment is not independent of te effect of capacity utilisation 14

18 profitability may become (relatively) less relevant as a predictor of future profitability wen te profit sare increases, so tat te sensitivity of investment to te profit sare declines. Unfortunately, it is unclear wy tis would be te case; Nikiforos refers to Kalecki (1971/1943) and asserts tat te limited size of a market may become more important for investment decisions, relative to te profit sare. But Kalecki (1971/1943) specifically mentions tat is argument applies to te sort period; e does not refer to te medium or long period tat te Kaleckian growt models represent. In te long run, te market size depends on equilibrium aggregate demand, wic itself depends on investment; it is tus strange to model profitability expectations as less sensitive to current profitability wen te latter increases, because of a limited market size. However, tat does not mean tat market size does not play any role in investment decisions in te long run. Nikiforos s (2016) second argument is more compelling: e points out tat finance may be no longer constrained by retained earnings wen a certain profit margin is reaced. Wen te profit sare becomes very ig, firms will ave suc an abundance of retained earnings tat a furter increase does not incentivise firms to invest more. Tis is because te market size and tus demand for firms output becomes a binding constraint. Looking at modern day tec firms, tis argument makes a lot of sense: companies suc as Apple, wic is known for its enormous stock of retained earnings, will not be able to invest more wen teir already uge profit margin increases, since tey can already invest as muc as tey deem fit. Te market size tus does not influence te relation between current and future profitability, but becomes more important relative to retained earnings, as te latter gradually ceases to constrain investment. Anoter reason for a declining effect of profits on investment can be found in te beavioural response of economic agents to structural canges. In te post-kaleckian model, functional income distribution affects aggregate demand troug te investment and saving function. However, a cange in te overall propensity to save also as an effect on te structure of te economy: since an equilibrium position implies tat saving and investment are equal, a iger propensity to save must be accompanied by a iger investment sare in total output. In a long run equilibrium, tis means tat te production of investment goods relative to consumption goods increases. Te question ten arises weter tis affects economic beaviour. Investment decisions are made before any of te potential cas flows tat result from tem appear; consumption, 15

19 on te oter and, is usually done out of wages (or oter types of income) tat are already earned 6. Investment terefore entails a iger degree of uncertainty; investors make decisions based on expectations of te future, wic is fundamentally uncertain, wereas consumers (mostly) make decisions based on tings tat ave already appened 7. Investment beaviour is terefore at least partly based on Keynes s (1936) famous animal spirits, and tus somewat less predictable tan consumption beaviour. Tis explains te fact tat investment is te most volatile component of aggregate demand (Blecker, 2016). A iger sare of investment in total output or more firms producing macines to make macines wit tus results in te fact tat more firms are basing teir investment decisions on te investment decisions of oter firms, and are ence facing ig uncertainty. It seems reasonable to assume tat tis ig level of uncertainty will ave a dampening effect on firms animal spirits 8. Te sensitivity of investment to profits may ten be affected negatively by an increase in te profit sare, since te latter causes te economy to sift from being consumption-based towards being investment-based. Combined wit Nikiforos s (2016) argument on te smaller role for profits in investment financing wen margins are ig, tis leads to te assumption of an investment function tat is nonlinear wit respect to te profit sare, suc tat its first order derivative is declining wen te profit sare increases (i.e. a negative second order derivative). Besides te investment function, Kaldor (1940) argues tat te saving function is nonlinear as well. According to Kaldor, ouseolds save muc less wen income is very low; tere is some amount of autonomous consumption. On te oter and, tose wit very ig incomes save muc more because some degree of saturation appears at ig consumption levels. Nikiforos (2016) reasons in a similar way regarding te relation between saving and te profit sare. He argues tat as te profit sare increases, te propensity to save out of profits increases as well, because no matter ow extravagant ric ouseolds are, wit respect to teir consumption, tere is only so muc tat tey consume (p. 398). Tis 6 Tis is of course not true for credit-based consumption expenditures. However, taking into account consumption credit does not cange te fact tat for most consumption, income is earned before te actual expenditure takes place, wic is not necessarily te case for investment. 7 Tis is not to say tat consumers do not ave to deal wit uncertainty, or tat teir consumption decisions are not affected by any form of uncertainty. Te point ere is not tat consumers suffer less from uncertainty tan investors; rater, tose observing te beaviour of bot groups of economic agents, are faced wit iger uncertainty regarding te investment decisions of firms. 8 Riddick and Wited (2009, p. 1764) note tat te effect of uncertainty on te propensity to save out of cas flow is empirically at least as strong as te effect of finance constraints. 16

20 argument closely resembles Keynes s (1936) absolute income ypotesis. Te elaborate debate about tis ypotesis will not be reviewed furter ere, but some notes on Nikiforos s interpretation are in order. As noted before, te propensity to save out of profits is in te post-keynesian and Kaleckian literature usually assumed to be iger tan te propensity to save out of wages. Tere are two reasons for tis: part of profit income is retained by firms, and terefore per definition saved, wile te remaining part is distributed to ouseolds. Tese ouseolds are usually ricer tan tose tat receive (only) wage income, and ricer ouseolds usually save a iger proportion of teir income, even if only because a smaller part of teir income is required for basic necessities of life (Hein, 2014, p. 273). Nikiforos extends tis static assumption to a dynamic one: e assumes tat te propensity to save out of profits increases wen te profit sare increases. Te rising profit sare most likely leads to iger personal income inequality. If one assumes tat iger income inequality leads to a larger gap between te propensities to save, ten Nikiforos s argument makes sense. However, tis argument by no means necessarily follows from te assumption tat ricer ouseolds save a larger part of teir income tan poorer ouseolds do at a specific point in time. Nikiforos essentially claims tat te propensity to save out of profits is a linear function of te profit sare, wic is a muc more far-reacing assumption tan te standard Kaleckian presupposition. In fact, it is very well possible tat te latter olds, wile at te same time te relation between te propensity to save out of profits and functional income distribution is completely different from wat Nikiforos supposes; tis depends on social and cultural norms (Prante, 2017). Furtermore, Nikiforos s (2016) teory of te propensity to save seems to disregard is own teory about te sensitivity of investment to profits. If firms are indeed no longer constrained by te availability of retained earnings wen teir profit margin is sufficiently ig, ten one would expect tese firms to distribute a larger part of teir profits. Tis would cause te propensity to save out of profits to decrease, wic could partly or completely offset te positive effect described above. As a result, te effect of a cange in functional income distribution on te propensity to save out of profits is uncertain. 17

21 4. Endogenous regime sifts in a simple Kaleckian model Nikiforos (2016) proposes a metod of incorporating is arguments on nonlinear beaviour in te saving and investment functions of te post-kaleckian model. In tis section, is suggestions will be applied partly: te model tat will be presented below includes an altered (nonlinear) investment function, but a standard post-kaleckian saving function. Te reason for tis is tat te arguments for a nonlinear investment function are simply stronger tan tose for a nonlinear saving function, as was explained in te previous section. Moreover, even if tere is, as Nikiforos suggests, a positive effect of te profit sare on te propensity to save, tere may also be a counterbalancing negative effect 9. Anoter difference between te model presented ere and te one by Nikiforos (2016), is tat functional income distribution is treated ere as being completely exogenous. Tis assumption most likely does not old in reality, but enables a clearer analysis of te effect of functional income distribution on growt and effective demand. 4.1 Assumptions and basic caracteristics Te model as te same basic caracteristics as te simple post-kaleckian model. For convenience, te main assumptions are reiterated ere: 1) output consists of a omogenous product, wic can be used bot as an investment good and as a consumption good; 2) tere is no overead labour; 3) te capital stock does not depreciate; 4) tere are no raw materials nor intermediate products; 5) tere is no tecnological progress and tere are constant returns to scale, so tat te capital-potential output ratio and te labour-output ratio are bot constant; 6) tere is only one production tecnique available, wic requires bot labour and fixed capital; 7) firms operate in an environment of oligopolistic competition, and determine teir prices by marking up unit labour costs; 9 Sticking wit a linear saving function also simplifies te analysis considerably; introducing a nonlinear saving function as well would make te matematics muc more complicated. Te qualitative results, owever, would not be very different. 18

22 8) firms usually operate below full capacity utilisation, so tat adjustment to canges in aggregate demand takes place troug quantities rater tan prices; 9) output is not constrained by te availability of labour, because tere are unemployment workers willing to provide teir labour power; 10) tere is no government expenditure; 11) tere is no foreign sector, tat is, te economy is a closed economy; 12) workers earn wages wic tey completely spend on consumption; capitalists earn profits wic tey partly save. 10 At its core, te model consists of te same equations as te standard post-kaleckian model presented in Section 2:. = 1 2, (4.1) = &, (4.2) 3 = 4 6!/ = 5 6. = , (4.3) > =? / = = + A, (4.4) Te only cange made ere is tat te coefficient A, wic represents te sensitivity of investment to te profit sare, is, following Nikiforos s (2016) suggestions, now defined as: so tat te accumulation function can be written as: D3 D1 D> D1 > > 0. (4.5) A = A N A I ; A N > A I, (4.6) > =? / = = + (A N A I ) = = + A N A I I. (4.4a) 10 A positive propensity to save out of wages can be introduced in tis model; tis will be elaborated upon in Section

23 4.2 Equilibrium and IS curves Te equilibrium rates of capacity utilisation and growt follow from te goods market equilibrium condition: > = 3, (4.7) = + A N A I I = , (4.7a) 1 = = + A N A I I, 5 6 > = 3 = (= + A N A I I ) (4.8) (4.9) Capacity utilisation is profit-led wen: D1 D > 0 2@A I A I I = 5 6 N > 0. (4.8a) Capital accumulation, growt and te rate of profit are profit-led wen: D> D > 0 3@A I I (A N I 2A I M ) > =@ + 2@A N. (4.9a) As becomes clear from tese equations, te level of te profit sare now partly determines te regime. Wereas in te standard post-kaleckian model, a cange in functional income distribution could only turn a conflictive regime in a cooperative regime and vice versa (see Section 2), suc a cange can now also turn a wage-led regime profit-led and te oter way around. Te IS curves tell a somewat more complicated story. As wit te standard post- Kaleckian model, two main constellations can be distinguised. Te first constellation, wic I will call te wage-led case, is sown in Figure

24 1 > (a) Figure 4.1: Utilisation (a) and growt (b) curves in te wage-led case (b) In tis case, te utilisation curve is strictly downwards sloping, as sown in Figure 4.1a, wit a decreasing absolute value of te slope. Te wage-led case terefore obtains wen te second order derivative of te equilibrium rate of capacity utilisation wit respect to te profit sare is positive: D I 1 D I > 0 = 5 I 6 2 I 5 6 N A I > 0. (4.8b) Figure 4.1b presents te growt curve in te wage-led case. Tis curve is linked to te capacity curve in Figure 4.1a, and also appears wen condition (4.8b) olds. Te sape of tis curve is determined by te same condition as tat of te utilisation curve in Figure 4.1a. Te reason for tis is tat te rate of capacity utilisation appears in te investment function, suc tat te sape of te curve in Figure 4.1a directly determines tat of te curve in Figure 4.1b. Te second constellation, wic will ereinafter be called te dynamic case, is sown in Figure 4.2. Tis constellation arises wen te second order derivative of te equilibrium rate of capacity utilisation wit respect to te profit sare is negative, i.e.: D I 1 D I < 0 = 5 I 6 2 I 5 6 N A I < 0 (4.8c) Tese curves ave similar, inverted U-type sapes. 21

25 1 > (a) Figure 4.2: Utilisation (a) and growt (b) curves in te dynamic case (b) Finally 11, a tird constellation (ere called te unresponsive case ) appears wen te second order derivative is exactly equal to zero, i.e.: D I 1 D I = 0 = 5 I 6 2 I 5 6 N 2 A I. (4.8d) Te utilisation curve in tat case is a straigt, downwards sloping line, wile te growt curve is a parabola wit a maximum; tis is sown in Figure Obviously, tere is a fourt case, wen A I = 0; te model ten becomes standard post-kaleckian and all te IS curves look te same as before. 12 Wit te expression for te equilibrium growt rate derived above, te parabola also appears = 0, no matter wat te values of te oter parameters are (as long as A I 0). Te equilibrium rate of growt is ten completely determined by exogenous variables, witout any feedback effect of capacity utilisation. 22

26 1 > (a) Figure 4.3: Utilisation (a) and growt (b) curves in te unresponsive case (b) 4.3 Comparative dynamics, distribution-ledness and regime sifts Te equilibrium outcomes of te model provide some interesting insigts. First of all, te utilisation curve in te dynamic case (Figure 4.2a) strongly resembles te one suggested by Taylor (1990), You (1994) and Palley (2013b). However, as wit oter versions of te post- Kaleckian model, tis outcome is not unique, and witout any knowledge of te real values of te exogenous parameters, tere is no reason to assume tat te utilisation curve actually as tis sape, and is not strictly downwards sloping. Terefore, in te remainder of tis subsection, te two different constellations will be analysed separately, witout furter considering te borderline tird situation of equation (4.8d) and Figure 4.3. In te wage-led case (Figure 4.1), te utilisation curve is not tat different from te standard post-kaleckian wage-led curve; te introduction of a nonlinear accumulation function seems to ave a limited effect, and te system is still more strongly wage-led for low levels of te profit sare, owing to te iger investment multiplier. However, te concomitant, somewat odd sape of te growt curve in Figure 4.1b sows tat growt is first strongly wage-led, ten profit-led, and ten wage-led again. Starting from a low profit sare, and redistributing income towards profits tus sifts te regime from wage-led to intermediate/conflictive and back to wage-led. Tese strange dynamics can be explained by te combination of te multiplier effect and te diminising sensitivity of investment to te 23

27 profit sare. A low profit sare means a low average propensity to save, and tus a ig investment multiplier, so tat te economy is strongly wage-led; as tis effect weakens wen te profit sare increases, te direct positive effect of te profit sare on investment takes over. Tis effect also weakens, but exponentially (by assumption), so tat te regime becomes wage-led again at a iger level of te profit sare, albeit less strongly wage-led tan before because of te lower investment multiplier. Canging te exogenous parameters affects te curves by sifting tem, but also by canging teir sapes. Increasing te propensity to save out of profits (5 6 ), or te A I variable as a dampening effect on aggregate demand and terefore sifts te curves downwards, wereas increasing te constant in te accumulation function (=), te sensitivity of investment to capacity utilisation (@), te capital-potential output ratio 2 or te sensitivity of investment to te profit sare (A N ) as a stimulating effect on aggregate demand, so tat te curves sift upwards. At te same time, an increase in 2 or A I strengtens te effect of capacity utilisation on investment 13, relative to profits, so tat te troug in te growt curve becomes smaller and te curve itself smootens to a more unambiguously wage-led sape; increasing A N or 5 6 as te opposite effect. Especially 5 6 strongly affects te sape of te growt curve, since it determines te investment multiplier as well as te sensitivity of te investment multiplier to canges in functional income distribution. Wen te difference between saving out of profits and saving out wages increases, te troug in te growt curve deepens. Needless to say, suc a deepening or smootening of te growt curve can cause te economy to sift from a cooperative to a conflictive wage-led regime. Tis is sown in Figure 4.4. In te dynamic case of Figure 4.2, te effect of te nonlinear investment assumption is immediately visible. Te utilisation curve as an inverted U-sape, instead of te strictly upwards sloping curve of te profit-led regime in te standard model. Capacity utilisation is tus profit-led for low levels of te profit sare, and wage-led for iger levels. Wat is more, te growt curve reveals te same pattern, suc tat a cange in functional income distribution can in tis situation sift te economy from completely wage-led to completely profit-led. Te multiplier effect is of course not absent in tis situation; it is te reason wy 13 Tat is, te effect on equilibrium investment. Wat is meant ere is tat a iger equilibrium utilisation rate as a stronger effect on investment tan a lower rate. 24

28 te profit-led part of te IS curves is muc steeper tan te wage-led part 14. Furtermore, te fact tat te two curves ave a similar sape does not mean tat tey completely overlap; terefore, an intermediate (i.e. conflictive) regime is still possible. Te next subsection provides a more elaborate discussion on tis. 1 > (a) (b) Figure 4.4: Effects of an increase in te propensity to save out of profits on equilibrium capacity utilisation (a) and growt (b) in te wage-led case In te dynamic case, canges in te exogenous parameters ave te same dampening and stimulating effects as in te wage-led case. However, tese effects can now be subdivided in two categories: te curves can sift upwards (=, A N ) or downwards (A I ), or tey can become steeper (@, 2) or less steep (5 6 ). As a result, stimulating (dampening) canges of te first, curve-sifting kind ( Type I, sown in Figure 4.5) make te economy less (more) wage-led or profit-led, depending on te level of te profit sare. Stimulating (dampening) events of te second kind ( Type II, sown in Figure 4.6), on te oter and, increase (decrease) te distribution-ledness of te economy. Moreover, suc events can sift te economy from profit-led to wage-led and vice versa, because tey move te maximum of te curve. 14 Te wage-led part of te curves appears at iger levels of te profit sare, so tat te multiplier is smaller and te stimulating or dampening effect of income redistribution more modest. 25