A. Shaikh February 12, 2007 A Proposed Synthesis of Classical and Keynesian Growth

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1 I believe that one can combine the eential propoition of Keyneian-type (KT) and what I call Claical- Type (CT) growth theorie in a imple way. All it take are three relation, two of which are common to both tradition, and a third which i alo implicit in both. The motivation for thi wa the recognition that both CT and KT theorie emphaize that accumulation i regulated by profitability. Yet KT theory find that profit-driven accumulation lead to peritent difference between actual and normal (minimum cot) capacity utilization. In CT theory, a in Harrodiantype (HT) theory, uch an outcome i not plauible becaue accumulation i only utainable when invetment expectation are roughly correct in the long run, i.e. when the actual rate of capacity utilization gravitate around the normal rate 1. But in the cae of HT theory, the latter outcome require that invetment i governed by thrift (a in Solovian growth theory), rather than by profitability. CT theory preume that it i poible to have profit-driven accumulation and elf-conitent invetment. But if the exiting literature i correct, we mut chooe one or the other. I would argue that there i imple way to make both outcome poible. The ecret lie in the treatment of buine retention ratio (the buine aving rate). To ee thi, conider an initial ituation in which there i ongoing accumulation at normal capacity utilization with ome initial private aving rate. In thi ituation, firm are financing their invetment from retained earning, from ale of new equitie and bond to houehold, and from bank loan correponding to their deired debt ratio. Now if the deired rate of accumulation were to rie, deired accumulation would exceed normal accumulation, which would require firm to eek additional finance. While their action may or may not induce houehold to raie their own aving rate (Kaldor, 1966, Appendix: A Neo-Painetti Theorem, pp ), firm can alo fill part of thi gap through a higher retention ratio 2 and the ret of it through a greater reliance on bank loan. The lat would inject demand into the ytem and raie the level of output a in the traditional multiplier, while the firt two would omewhat raie the overall aving rate. Given that accumulation repond to both normal profitability and the gap in capacity utilization, if thi proce i table (which i demontrated below) it will continue until actual accumulation gravitate around the new profit-driven deired rate. It turn out that the character of the long run ituation depend olely on whether the buine aving rate repond at all to the gap between deired and normal accumulation. If it doe even a bit, then the new long 1 A Garegnani (1992, p. 56) note, invetment i driven by it expected rate of return at expected normal utilization i.e. by it expected normal rate of profit. 2 Since the buine aving rate i a component of the overall aving rate with a weight equal to the profit hare, Eichner and Wood and other uppoe that the profit-hare, i.e. the markup, i raied at thi point to raie the overall aving rate. But for thi to work over the long run, the real wage rate mut be aumed to be entirely paive: i.e. a fixed money wage even in the long run, o that the real wage fall and the real profit hare rie when markup rie. If worker fight to maintain a particular hitorically-determined tandard of living, the money wage cannot be taken to be fixed in the longer run. 1

2 run i characterized by profit-driven accumulation at roughly normal capacity utilization, which i the CT outcome. Converely, the KT tate (profit-driven accumulation with capacity utilization different from normal) obtain only if the retention ratio doe not repond at all. In what follow, the demontration of thee claim i cat at the mot abtract level, becaue that i where the real difference arie. Let I = invetment, S = aving, = the aving propenity, Y = output, Yn = normal capacity (at the lowet point on the cot curve), Ymax = maximum technical capacity (engineering capacity), K = capital tock, g K = the accumulation rate (growth rate of K), u = capacity utilization = Y/Ymax, u n = normal capacity utilization (determined by the lowet cot point on the cot curve) = Yn/Ymax, g K (r n ) = the rate of accumulation at the normal rate of profit (r n ), and R = Ymax/K. The firt two equation below are common to both CT and KT (particularly Pot Keyneian, PK) theory: the hort run equilibrium condition; and what Lavoie call the tandard PK accumulation function, written in uch a way a to eparate out accumulation at normal profitability and accumulation reponding to change in capacity utilization 3 through the parameter h, which i ubject to the tandard PK retriction required for tability (ee Appendix A). 1) I = S = *Y [Short run equilibrium] 2) g K = g K (r n ) + h (u - u n ) [CT and PK accumulation function] The third equation ret on the notion that the buine aving rate repond to the gap between deired and normal accumulation. For intance, Kurz (1992, p. 86) ugget that buine "aving ratio may themelve depend on the rate of accumulation" o that "in time of relatively high accumulation firm [may] increae the proportion of retained profit". The argument can alo be derived from Marx' dicuion of the difference between the circuit of revenue (in which houehold aving reide) and the circuit of capital (in which there i retained earning, i.e. buine aving). To highlight the iue at hand, both the houehold aving rate and the profit-hare are taken to be contant, o that the private aving rate alo repond to the accumulation gap when the buine aving rate doe 4, via ome poitive parameter σ 5. 3 The general PK accumulation function ha the form g K = F(g K (r n ), u). Lavoie (1996, p. 119) lit it a g K = a + b u + c r n, which we can write a g K = g K (r n ) + h (u - u n ), where g K (r n ) = c 0 + c r n, c 0 = (a + b u n ), and h = b. 4 Aggregate output Y = W + P = (W + DIV) + RE = Y h + S b, where W = the wage bill, P = profit = DIV + RE = dividend + retained earning. Total aving i the um of houehold aving out of houehold income (S h = h Y h = h (Y RE)) and buine aving RE out of profit (RE = ρ P), where h and ρ are the houehold and buine aving (retention) rate, repectively. The aggregate aving rate S/Y = [ h (Y 2

3 3) ' = σ (g K - g K (r n )) The ytem formed by equation 1-3 gravitate around normal capacity utilization (the proof i in Appendix A). Figure 1-2 depict it characteritic repone to a hock to the invetment level at t = 10 and a hock to the accumulation rate at t = 30. Note that depite both type of hock, the ytem converge to u = 1 (normal capacity utilization) becaue the aving rate i endogenou. Thu over the long run accumulation i driven by normal profitability and capacity utilization gravitate around it normal level. Converely, if the aving rate reaction parameter i fixed at zero (i.e. the aving rate i aumed to be independent of the accumulation gap), the ytem revert to equation 1-2 alone, and one get all the tandard PK reult: the long run rate of capacity utilization i different from normal, and both hock will raie the capacity utilization rate permanently becaue the aving rate i fixed (Figure 3-4). Several thing follow from the endogeneity of the buine aving rate. Deired invetment i driven by it underlying normal profitability, and aggregate aving adapt itelf to aggregate invetment. Thee two propoition are completely conitent with a claical approach and alo with the "the central thei of the General Theory that firm are free, within wide limit, to accumulate a they pleae, and that the rate of aving of the economy a a whole accommodate itelf to the rate of invetment that they decree" (Robinon, 1962, pp ) 6. However, becaue the claical accommodation i partially achieved through a higher aving propenity, the overall multiplier effect will be maller than thoe implied by traditional Keyneian theory. RE) + ρ RE)/Y = [ h + ρ (1- h )(P/Y)]. Then even if the houehold aving rate and the profit hare are contant, the aggregate aving rate will repond to any finance gap if the retention rate doe. 5 Harrod ugget a aving rate repone function very imilar to that in equation 3. But hi argument concern the deviation of the hort run aving rate () from the long run "normal" rate ( n ). The latter i determined by the normal aving propenitie of houehold and buinee, and by the normal profit hare, a hown in footnote 4. Thi normal aving rate, along with the normal capacity-capital ratio R n, determine the long run warranted rate of growth ( n u n R n ). Harrod think of the actual rate of growth a gravitating around the long run normal warranted rate, o a certain range of difference between the two i normal. But he alo make "cattered" reference to the poibility that houehold and buine aving rate will deviate from their long run value when the actual rate of accumulation i "abnormally" different from the long run warranted rate. For intance, if the former i abnormally lower than the latter, aving rate will alo fall, which will lower the hort run ("pecial") warranted rate ( u n R) and help narrow the gap (Pugno, 1998, pp. 152, ). Thi i a tabilizing effect, and if it were large enough, it would enure gravitation around the long run warranted path itelf. But the centrality of the latter implie that in the long run accumulation i driven by thrift, not by profitability. 6 It hould be noted that when Robinon peak of "rate" of aving and invetment, he mean their level i.e. their flow per unit time. 3

4 A in Harrod and the claical, the actual rate of capacity utilization will gravitate around the normal rate (Figure 2). Thi doe not obtain in the Keyneian ytem (Figure 4) A in Keyneian theory, a rie in the autonomou level of invetment with no change in it growth rate will raie the level of the long run output path without changing it growth rate (the invetment hock in Figure 1 and 3). But becaue the aving rate alo rie in the claical cae, the correponding effect on output i much maller than in the Keyneian cae. A in Keyneian theory, a rie in the normal rate of profit will raie the normal rate of accumulation (ee equation 2), which will raie the long run rate of accumulation (a hown by the lope of lny in Figure 1 and 3). Finally, a rie in the houehold aving rate will have no permanent impact on the rate of accumulation unle it happen happen to alter the profit rate (or the interet rate, when the normal profit i more concretely pecified a net of interet), becaue otherwie it will imply reduce the retention ratio needed to upport a given rate of accumulation. Thi might be viewed a an alternate path to Kaldor' neo-painetti theorem (Lavoie 1998, p. 421). The important point i that thi claical ynthei allow u to preerve central Keyneian argument uch a the dependence of aving on invetment and the regulation of invetment by expected profitability, without having to claim that actual capacity utilization will peritently differ from the rate deired by firm. It i true that the cope of the multiplier i omewhat reduced becaue part of the adjutment take place through a variation in the aving rate. But given that thi ame mechanim lead to the gravitation of capacity utilization around the normal level, I would argue that the overall benefit i ubtantial. The effect of technical change, wage rate and interet rate, international factor, and fical and monetary policy, can then proceed from thi foundation. 4

5 Figure 1: Claical accumulation, log of invetment (I) and output (Y) ln Y Invetment level hock Acccumulation rate hock ln I Time Figure 2: Claical accumulation, aving rate () and capacity utilization (u) u (left axi) (right axi) u Invetment level hock Accumulation rate hock Time

6 Figure 3: Keyneian accumulation, log of invetment (I) and output (Y) ln Y ln I Invetment level hock Acccumulation rate hock Time Figure 4: Keyneian accumulation, aving rate () and capacity utilization (u) u (left axi) Invetment level hock Accumulation rate hock 0.10 u (right axi) Time

7 Appendix B: Stability of profit-driven accumulation with an endogenou buine aving rate Two baic relation are common to the PK and CT dynamical ytem: hort run equilibrium (I = S), which implie a relation between the rate of accumulation, the aving rate and the rate of capacity utilization; and an accumulation function uch a the tandard PK function. The relevant equation are reproduced below a they appear in the text. Common Relation 1) g K = R u [Short run equilibrium: I = S] 2) g K = g K (r n ) + h (u - u n ) [the tandard PK accumulation function] Claical Keyneian and PK 3) ' = σ (g K - g K (r n )) 3a) ' = 0 The ole difference between the two dynamical ytem then arie from their treatment of the buine aving rate. If we take the houehold aving rate and the ditribution of income a given, o a to iolate the iue at hand, the difference between the two approache i clear: the PK ytem appear a a pecial cae of the CT ytem when we aume a fixed buine aving rate. Thu the former can therefore be derived from the latter by etting the aving rate adjutment coefficient σ = 0 in equation 3, in which cae profit-driven accumulation yield the tandard PK reult that capacity utilization remain peritently different from the normal rate. Converely, any reponivene at all on the part of the buine aving rate (σ > 0) convert the PK ytem into a CT one, and it become poible to have both profit-driven accumulation and normal capacity utilization over the long run. The general cae (σ > 0) yield a nonlinear differential equation in the endogenou aving rate 7. 4) ' = σ g K (r n ) [(1 (/ n )]/[((/ n ) ( n R/h)) 1] 7 Since (g K - g K (r n )) = h (u - u n ) from equation 2, and u = g K / R and u n = g K (r n )/( n R) from equation 1, (g K - g K (r n )) = h [(g K / R) u n ] = h [(g K / R) (g K (r n )/ R) + (g K (r n )/ R) u n ] = (h/ R) (g K - g K (r n )) + h (g K (r n )/R) [(1/) (1/ n )], ince (R u n )/g K (r n ) = 1/ n. Collecting term give (g K - g K (r n )) = h (g K (r n )/R) [(1/) (1/ n )]/[1 h/( R)] = h (g K (r n ) [(1 (/ n )]/( R h) = g K (r n ) [(1 (/ n )]/( (/ n ) ( n R/h) 1). Subtituting thi into the aving rate adjutment equation 3 give u equation 4, a nonlinear differential equation in the endogenou aving rate. 7

8 Suppoe that h < n R, o that [((/ n ) ( n R/h)) 1] > 0 when n. Then in equation 21 a n from above, the denominator of the expreion in quare bracket remain poitive and the numerator goe from negative to zero, o that ' goe from negative to zero alo. Finally, for < n, a h/r < n, ' approache infinity becaue the numerator i poitive while denominator i alo poitive and approache zero. The phae diagram correponding to equation 4 (Figure 5) therefore ha a ingle table poitive equilibrium at = n, a long a h < n R. It i ueful to note that h < n R = g K (r n )/u n i alo the tability condition for the PK model (Dutt, 1997, p. 246;Lavoie, 1996, p. 122). Finally, for the imulation reult which were diplayed in Figure 4-5 in the text, equation 2-3 were written a the difference equation g K = g K (r n ) + h (u(-1) - u n ) and = (-1) + σ h h (u(-1) u n ), ince (g K - g K (r n )) = h (u(-1) - u n ), with parameter value R = 0.5, g K (r n ) = 0.03, h = 0.01, σ = 2, u n = 1, and initial value at equilibrium level g K (0) = g K (r n ), u(0) = u n, and (0) = n g K (r n )/R u n. Invetment wa derived a I = g K K(-1), output a Y = I/, and capital a K = I + K(-1), with initial value I(0) = 10, K(0) = The initial equilibrium run i broken at t = 10 by a permanent addition to invetment of 2.54 (which i 10 percent of invetment in the prior period), and at t = 30 by a rie in the profit-driven component of accumulation g K (r n ) from 0.03 to Figure 4 diplay the path of ln I and ln Y, while Figure 5 thoe of and u. Figure 5: Phae Diagram, Endogenou Saving Rate ' (h/r) n 8

9 Reference Dutt, A.K. "Equilibrium, Path Dependence and Hyterei in Pot-Keyneian Model," P. Areti, G. Palma and M. Sawyer, Capital Controvery, Pot-Keyneian Economic and the Hitory of Economic Thought: Eay in Honour of Geoff Harcourt. London: Routledge, 1997, Garegnani, Pierangelo "Some Note for an Analyi of Accumulation," Joeph Halevi, David Laibman and Edward J. Nell, Beyond the Steady State: A Revival of Growth Theory. New York: St. Martin' Pre, 1992, Kaldor, Nichola. "Marginal Productivity and the Macroeconomic Theorie of Ditribution. Comment on Samuelon and Modigliani," Finance, Invetment, and Steady Growth. 1966, Kurz, Heinz. "Accumulation, Effective Demand and Income Ditribution," Joeph Halevi, David Laibman and Edward J. Nell, Beyond the Steady State: A Revival of Growth Theory. New York: St. Martin' Pre, 1992, Lavoie, Marc. "Travere, Hyterei, and Normal Rate of Capacity Utilization in Kaleckian Model of Growth and Ditribution." Review of Radical Political Economic, 1996, 28(4), pp Pugno, Maurizio. "Harrod' Economic Dynamic a a Peritent and Regime-Changing Adjutment Proce," Giorgio Rampa, Luciano Stella and A.P. Thirlwall, Economic Dynamic, Trade and Growth: Eay on Harrodian Theme. London: Macmillan Pre, 1998, Robinon, Joan. Eay in the Theory of Economic Growth. London: Macmillan,