Cambridge Journal of Economics 1988, 12, 339-354

Finance, saving and accumulation

Peter Skott*

The availability of finance is of central importance for any theory which views auton-omous investment as the major determinant of production and employment. Investmentneeds to be financed and if, say, saving decisions affect the conditions of financing newinvestment, then it might be difficult to maintain the traditional Keynesian view ofsaving as the passive and accommodating variable in the face of independent and activeinvestment decisions.

Given the importance of the issue, it is hardly surprising that saving and finance havereceived considerable attention in the literature and that the issue keeps resurfacing. Thepresent paper has been stimulated by the recent debate following Asimakopulos' 1983article in this Journal. Asimakopulos suggests that 'the independence of investment, andthe finance that makes investment possible, from saving is not as robust as Keynes stated.The investment market can become "congested through shortage of saving" even in aclosed economy' (p. 230). He concludes that 'there may be limits, related in some way tothe propensity to save, to the extent to which firms are in a position to increase their rate ofinvestment even if short-term credit is available to finance such an increase' (p. 232).

This conclusion is at odds with received Keynesian and Kaleckian wisdom, andAsimakopulos' paper has provoked a number of comments.1 Asimakopulos does notformalise his argument in the context of an analytical model, but stock-flow issues areclearly at the centre of the argument. Unfortunately, the standard Keynesian analysis payslittle attention to financial stocks and it is thus difficult to assess the validity and empiricalimportance of Asimakopulos' strictures.

In this paper I wish to set up a simplified model which by integrating financial and realvariables may help to elucidate essential aspects of the problem raised by Asimakopulos. Itshould be pointed out, however, that although I shall examine the effects of changes insaving parameters on finance and investment, I do not intend to address the details ofAsimakopulos' argument. Furthermore, I shall look at some broader issues not discussedby Asimakopulos. Whereas the current debate on finance and investment has focused onshort-run problems, the present model can be used to analyse the interaction betweenfinancial and real variables in the short run as well as over longer periods.

The model is firmly in a Keynesian/Kaleckian tradition. It is particularly close toKaldor's 'neo-Pasinetti' model (Kaldor, 1966) in that the clear distinction between finan-cial assets (held by households) and real assets (controlled by firms) plays a fundamental

•University of Aarhus. I wish to thank Michael Anyadike-Danes, Paul Auerbach, Victoria Chick andGeoffrey Harcourt for comments on an earlier version of this paper. Comments and suggestions from ananonymous referee have also been extremely helpful.

1 Graziani (1984), Kregel (1984-85,1986), Snippe (1985), Terzi (1986), Richardson (1986), Asimakopulos(1986), Davidson (1986).

0309-166X/88/030339 +16 803.00/0 © 1988 Academic Press Limited

340 P. Skott

role. But the model differs from Kaldor's in important respects. First, Kaldor does notconsider the feedback from households' saving and finance decisions to the determinationof production and investment. Second, in analysing these feedbacks the present modeldeparts somewhat from simple post-Keynesian distribution theory:1 the share of invest-ment in output will determine the growth rate of output rather than the distribution ofincome. Distribution, in turn, is determined in a Kaleckian manner: firms apply somegiven mark-up factor to unit variable cost.2 The third difference concerns the specificationof household behaviour. Whereas Kaldor posits given saving propensities for the differentincome categories, I shall model the saving behaviour of households explicitly in terms ofdesired financial stocks. The present paper, finally, will give greater attention to firms'financial constraints and to the influence of the overall monetary regime, the analysis ofthese aspects having some similarities with that of Wood (1975).

The basic assumptions of the model can be described as follows. There are three types ofagents, firms, banks and households. Firms decide the amounts of employment, produc-tion and investment. The decisions are based on the maximisation of expected profits butit is not assumed that expectations will always be fulfilled. Firms obtain finance from threedifferent sources, retained earnings, new issues and bank loans, and two different behav-ioural patterns are analysed. Firms may either be of 'type A' and set a constant retentionratio and a constant ratio of new issues to the stock of existing securities. Alternatively,they may adjust the retention ratio and the amount of new issues so as to make each sourceof finance cover some constant desired proportion of the total financial requirement. Ishall refer to firms which act in this way as 'type B' firms.

Banks extend loans to firms, and it is assumed that firms are never quantity constrained:they can borrow as much as they wish at the prevailing interest rate. But this assumption iscompatible with a range of different monetary regimes, and two polar cases are examined.The first is the Wicksell case where the rate of interest is kept constant over time and theamount of loans (the money supply) adjusts endogenously. The second is the monetaristcase which assumes that banks (can and do) adjust the interest rate in such a way that firmsare induced to expand their bank liabilities at some given constant rate.

Households, finally, supply labour, consume output and hold financial assets. Theremay be unemployment but households are not quantity constrained in any other market.

As far as the questions raised by Asimakopulos are concerned, the main conclusions areas follows. A rise in the average propensity to save will always, as claimed by Keynesianorthodoxy, have a deflationary impact on short-run production and employment. Some ofthe parameters which influence the saving propensity will also, however, affect the finan-cial valuation of firms, and changes in these parameters will have both a saving effect and avaluation effect. If the valuation effect dominates, then an increase in the saving cumvaluation parameter will induce higher levels of investment. Of course, it has never beendenied that saving behaviour can have delayed effects on investment. Such delayed effectsare part of the Keynesian (Harrodian) story of growth. The interesting point is the direc-tion of the effects. In traditional Keynesian/Harrodian theory, the lagged effect ofincreased saving propensities is to reduce investment, as effective demand problems leadto excess capacity. The influence of valuation effects allows the possibility that thedirection of the lagged effect may in some cases be reversed.

1 See Kaldor (1956) and Robinson (1962). The same basic distribution mechanism survives in Kaldor'sneo-Pasinetti model.

2 See Kalecki (1954). Kriesler (1987) and Basile and Salvadori (1984-85) are recent discussions of Kalecki'sdistribution theory. See also Skott (1989B), ch. 8.

Finance, saving and accumulation 341

The paper is in 7 sections. Section 1 presents the model. Section 2 analyses the short-run behaviour of the economy. Section 3 describes the determination of desired capitalutilisation and derives the wanranted growth path. Section 4 introduces type B assump-tions of firms' financial behaviour and Section 5 looks at the implications of a monetaristbanking regime. The effects of changes in the parameters are examined in Section 6, andSection 7 summarises the conclusions.

1. The model

At any given moment the level of production and employment are predetermined by pastproduction and employment decisions. But current decisions by firms determine the rateof change of output and employment—and thus the future levels of Y and L—as well asthe rate of investment, / . It is assumed that these decisions are based on profit maximisa-tion and that the constraints on the maximisation are as follows.

The production possibilities are given by a fixed coefficient production function,

Y=min{\L,oK} (1)

and marginal cost is thus equal to unit labour cost when there is spare capital capacity.The conjectured demand function of each individual firm is downward sloping and hasconstant elasticity,

p(Y) = DY"? (2)

where p is the price of output and D is a positive constant.Firms with positive pure profits face a threat of new entry, and although new entry will

not affect the current level of demand—entry is not instantaneous—it will reduce futuredemand: the expected future value of the parameter D (and possibly also the inverseelasticity of demand, y) will be affected, and if firms recognise this possibility then it will bereflected in their current behaviour.

The literature on limit pricing has suggested that current price and output decisionsmay be affected by the threat of entry, but here I shall take a different approach. FollowingSpence (1977), it is assumed that firms use excess capacity to deter new entry and thatfirms are thus free to pursue the pricing and output policy which maximises short-runprofits. When there is excess capacity this maximisation problem is given by

max pY-wL (3)s.t.

and we get

(4a)

1/ir (4b)

These short-run equilibrium values will not always be realised. The level of productioncannot be changed instantaneously in response to unforeseen demand conditions, andfirms' demand expectations will not in general be satisfied. Abstracting from stocks, thecurrent value of D can however be inferred from observed current values of Y and p. Fromequation (2) it follows that

342 P. Skott

where u is the utilisation rate of capital and subscripts 0 indicate current, observed values.How much excess capital capacity is needed to deter entry? I assume that the desired

amount of excess capacity is determined by the condition that the conjectured demandprice at full capacity utilisation be equal to average total cost at full utilisation. Therationale behind this assumption is that the firm expects entry to be 'very rapid' unless it isable to preempt positive pure profits for the entrants by expanding its production to thefull capacity level.

If each firm takes the nominal wage rate as well as the cost of finance, c, the rate ofdepreciation, 5, and the cost of new capital goods, pk, as parametrically given, we can use(1), (2) and (5) to derive expressions for the conjectured demand price at full capacity andtotal unit costs at full utilisation, and the condition determining desired utilisation can bewritten as

p(uuK)r(aK)-" = w/X+pk(c + S)la (6)

Assuming that the price of capital is equal to the general price level, pk will be equal top forthe representative firm and we get

i/ = w/plpi+(c + 5)/a (7)

The utilisation rate determined by (7) will not necessarily be realised in short-runequilibrium. Output adjusts very much faster than the capital stock to unanticipatedchanges in demand and utilisation will therefore usually deviate from the desired level.Equation (7) does, however, impose restrictions on the properties of the investment func-tion: persistent deviations of the utilisation rate from the desired level will lead to changes inthe rate of accumulation. The desired and actual rates of utilisation must therefore be equalin steady growth, and the share of in vestment in output is related to the rate of utilisation (aswell as to the technical output capital ratio and the rate of growth). For present purposeswe shall not need to impose additional structure on firms' investment behaviour.

Investment needs to be financed and, by analogy with the budget constraint ofhouseholds, firms face a financial constraint,

pI = sp(P-iM) + eNft+MM (8)

Equation (8) says that the flow of investment expenditure (p/) must be covered by the sumof retained profits (sp(P—iM)), the proceeds of new issues (eNlfy and the increase in bankloans (MM). P is total profits, i is the interest rate on bank loans and M the amount of bankloans, N is the existing number of securities, e is the price of securities, and the notation " isused to denote logarithmic derivatives (growth rates). The parameters sp, N and M reflectthe financial decisions of firms but the choice of sp, $ and M may be subject to additionalfinance constraints. In sections 1-3 it is assumed that the sp and ft are given constants andthat j p > 0, $ ^ 0. Section 4 makes both these parameters depend on the rate of investment,and in Section 5 banks fix M = m thus restricting the financial options of firms.

The financial decisions of firms are not derived from profit maximisation. Indeed itwould be difficult to do so. In a simple Modigliani-Miller world, the valuation of anindividual firm is independent of its financial structure, and profit maximisation thereforegives no guidance to the value of sp and N. Outside the unrealistic Modigliani-Millerworld, the valuation will be affected by financial decisions, but it is difficult to say exactlyhow, and in any case socio-institutional and historical factors are likely to be important inthe determination of'prudent' (optimal) finance.1

1 See Wood (1975) for a non-neoclassical account of the determination of the financial parameters.

Finance, saving and accumulation 343

With respect to banks, it is assumed that there are no costs involved in banking.Furthermore, lending and borrowing rates coincide and interest payments by firms tobanks are exactly equal to interest payments received by households: neither firms norhouseholds hold cash, firms have overdrafts with banks and households have currentaccounts. Banks thus have neither costs nor profits.

Households receive wage income as well as a return on their financial wealth. They ownno physical capital goods and their (non-human) wealth is held in the form of bankdeposits and securities. Interest is earned on the bank deposits, and the return on securi-ties comprises both dividend payments and capital gains. Household incomes are eitherspent on consumption or used to augment their financial assets. The desired stocks offinancial assets are related to current income flows, and the rate of saving adjusts so as tomaintain these desired stock flow ratios.

Algebraically, the model of household behaviour is as follows:

(9)

a(P-iM) = eN (10)

$W = M (11)

where C is consumption in real terms, W represents aggregate wage income, N and M arethe number of securities and the bank deposits owned by households, and e is the price ofsecurities.

Equation (9) is households' budget constraint: the flow of wage income (W), dividends((1—5p) (P—iM)), capital gains (eNi) and interest receipts (lAf) is either spent onconsumption (pO) or added to the stock of financial wealth. The behavioural assumptionswhich determine consumption and saving decisions are described in equations (10) and(11). The two equations specify relations between stocks of financial assets and currentincome flows, and the flow of household saving is thus determined by changes in incomeflows and in the value of financial stocks. It is assumed [eq. (11)] that the demand formoney is proportional to total wage (and salary) income. This minor modification ofsimple quantity theory assumption is motivated by the fact that if the demand for money isa transaction demand then relatively unstable income components like distributed profitsmay not have an important influence,1 and furthermore, low income households withoutany property income are likely to have a relatively high ratio of money to income.

The demand for financial securities [eq. (10)] is assumed proportional to the level ofprofits net of interest payments. This specification has the virtue of simplicity. It may alsohave a somewhat neoclassical flavour: if the level of profits is given then share valuation isindependent of firms' pay-out decisions. But in spite of the neoclassical flavour we shallget quite non-neoclassical results, and in fact no important conclusions of the modeldepend on the precise specification. It would be easy to relate eN to, say, the sum of wageincome and dividends or to total consumption, and this change would not affect thequalitative results of the analysis.2 It may seem unreasonable, however, to assume that aand p are independent of the relative rates of return on financial assets. The returns onbank deposits and securities are i and [(1 — s^/a + e], respectively. With the exception ofSection 5, it is assumed that i is fixed so that if the expected rate of appreciation of

' Dividends and capital gains of individual share owners may be volatile even if the average share of profits isquite stable. And, of course, if the average share of profits in income is constant then a constant incomevelocity of money implies that the ratio of money to wages will also be constant.

1 See p. 353 n. 1 below for a minor qualification. An alternative specification is used in Skott (1981) wherethe demand for both money and securities is related to nominal consumption expenditure.

344 P. Skott

securities is constant then the expected returns on both assets are in fact constant. As afirst approximation it may therefore not be too misleading to treat a and P as constantparameters.

Finally, with respect to the labour market and the formation of money wages, I shallassume that money wages are constant, i.e. that

w = 0 (12)

This is not an attractive assumption but it simplifies the analysis; Skott (1989B) allows forendogenous money wage determination.

2. The short term: output adjustment

Equilibrium in the product market requires that

Y=C+I (13)

and by definition we have

P=pY-W (14)

Equations (13) and (14) together with (9)-(12) determine n, the share of profits in income,as a function of decision variables of the firm sector (/, Y, Y, N, sp) and householdbehaviour (a, P),

H = [ ( / / y -P (? - i (* p + a^] / [ i p + a ^ - P ( ? - t ( 5 p + aiQ))] (15)

The solution values for the other endogenous variables of (9)-(14)—C,p, P, M, e—can befound by substitution of (15) into (9H14).

The interpretation of the equations is as follows. Confronted by particular values of thevariables under the direct control of firms, the accommodating variables M, e and p (or n)adjust so as to make households wish to consume exactly Y — I and hold the total numberof securities, N, offered by the firm sector.

The behaviour of households, however, and in particular the values of the accommodat-ing variables, will give a signal to firms, thus affecting firms' decisions in subsequentperiods. The market clearing price, p, for instance, may be above or below firms' short-runsupply price as determined by equation (4a). Any such deviation will induce changes in thelevel of production: production will increase (faster than trend) if the supply price is belowactual price, or equivalently, if actual output is below desired output, and production willdecrease if supply price is above actual price.

Although an increase in investment must necessarily be accompanied by an identicalreduction in consumption in the ultra short run where the level of output is predeter-mined, this is no longer so in the short run. The rate of investment is still treated as anexogenous variable in the short run and the share of profits must satisfy equation (15) ateach moment. But in a short-run equilibrium, output has been given time to adjust to thenew rate of investment and, as a result, the short-run equilibrium is characterised by apositive multiplier relation between investment and consumption. From equation (4a) itfollows that in short-run equilibrium the share of profits will be equal to y, and rearranging(15) and setting n = y we get

p p (16)

If Y = 0 this simplifies to

Finance, saving and accumulation 345

-(l-Y)Pi)(*p + a2Q)]/ (17)

The expression l/[(y — (1 — y)PO (sp + a$)] in (17) is the investment multiplier in thismodel. Note that the size of the multiplier depends on the financial decisions of firms (/tfand 5p) as well as on the saving and portfolio choices of households (a and P).

Equation (17) defines a standard short-run equilibrium where the rate of investmentand the money wage rate are both constant, and where output and employment have hadsufficient time to adjust fully to their equilibrium levels. If investment is not constant, amodified short-run equilibrium may nevertheless exist. This modified equilibrium allowsvariations over time in investment and production but retains the condition that the actualprice equals the supply price. Algebraically, equation (16) describes the relation betweenI, Y and Y which ensures that the product market clears at the desired supply price, i.e.that re = y. Should, however, the growth rate of output fail to adjust in accordance with (16)then there will either be quantity rationing or accommodating variations in the profit share[cf. eq. (15)].

3. The medium term: utilisation and warranted growth

The degree of capital utilisation must, as argued in Section 1, be at the desired level along asteady growth path. Otherwise, firms would wish to speed up or slow down the rate ofaccumularion. The desired utilisation rate is given by (7), and in modified equilibrium wehave

wlp = (l-y)k (18)

The conjectured cost of finance, c, can also be calculated. It is related to the share ofprofits, the value of Tobin's q {q) and the (expected) growth rate of demand,1

c = yi«yfa + C?f+5) ( 1 - 1 / 0 - 8 (19)

where^f is the expected growth rate of demand of the representative firm. The second termon the RHS of (19) appears because future increases in demand lead to equiproportionateincreases in earnings and in the desired capital stock, and if q> 1 then the cost of invest-ment is less than the value of the associated increase in earnings. This anticipated differ-ence between the financial valuation and the cost of future gross investment is reflected inthe current valuation of the firm and hence in the relation between the cost of finance andthe value of Tobin's q.

Using (10) and (11) we get an expression for Tobin's q

« (20)

and substituting (18)-(20) into (7), this equation can now be rewritten1 Tobin's q gives the ratio of financial valuation to replacement cost. Financial valuation of the firm is the

sum of equity valuation and bank loans. Current dividends are (1 —s^ (P—iM), and if it is assumed thatdividends are expected to grow at the same rate as the market for the firm's product (g,), then equity valuation,eN, is given by

tN=[ (1 - sj (jrou - iMIPoK,)PoK0 exp^) exp( - (tf + p)»)df = (1 - Jp) (ncu - iMJ<j>JCa)PoKJ[ti +p-g,]

where p is the return on equity and where exp{ — /?f) is the share of dividends at time t which accrues to shareswhich had been issued already at time 0. The average cost of finance can now be written as

where we have used the finance constraint, equation (8).

346 P. Skott

y - ( l -Y)P0) ] ) (21)

Equation (21) has two solutions in u but only one of these is economically meaningful.This value of u, u, is less than unity fora(P(l — Y) + a(y — (1 — y)PO))> 1 (or equivalently,for q> 1 when u= 1). (A proof of these propositions is available from the author onrequest.) Since, by definition, utilisation rates belong to the unit interval, the desired rateof utilisation, u*, becomes

u* = m\n{\,u) (22)

The interpretation here is straightforward when one recalls that excess capacity isdesired in order to deter entry. If q > 1 (for u = 1) then pure profits can be made and desiredutilisation rates are below unity; the higher the value of q (at u= 1) the higher are pureprofits and the lower therefore is the desired degree of utilisation. If on the other handq < 1 (for u = 1) then profits cannot cover the costs of capital at any rate of utilisation andthere is therefore no need to maintain excess capacity to deter entry, u* = 1. Empirically,one rarely observes full capacity utilisation, and then only at the peak of the cycle, and Ishall assume that u* < 1.

Utilising the steady growth assumption, equation (16) can be rewritten

M=l/a(£ + 6)/[Y(sp + c ^ + (l-Y)Pte-»(sp + atf))] (23)

It seems reasonable to suppose that the expected rate of growth of the representative firm,gp is related to the growth rate of the economy, £, and for simplicity I assume xhatg{=g.1

We now have two equations, (21) and (23), to determine the growth rate and theutilisation rate in steady growth equilibrium. These equations will not necessarily yield aunique steady growth solution (a unique warranted path), and for some parameter valuesno solution exists. The sign of A = y(sp + aft) — (1 -y)$i(sp + aft) — 5(1 — y)P is importanthere, and for all empirically reasonable parameters A>0. Concentrating on this case(A > 0), it can be seen that y>A+uy(\— y)P is a sufficient condition for the existence of asteady growth path.2 I shall assume that this condition is satisfied and that there is aunique steady growth path.

Harrod believed that a capitalist economy faces two problems: inequality between thewarranted growth rate and the growth rate of the labour force and, secondly, instability ofthe warranted path. Neither the growth of the labour force nor the rate of unemploymentplays any role in the determination of the warranted rate by equations (21) and (23).Harrod's first problem thus reappears in the present model, but is the warranted growthpath stable?

In order to examine this question we assume that initially the economy is moving alongthe warranted path but that for some reason the rate of accumulation then increases abovethe warranted rate. Inspection of equation (16) reveals that—since au is predetermined—the effect of this increase is to raise the growth rate of output and that, furthermore, ? > £(since A > 0). It follows that an increase in R above the warranted rate leads to a positiverate of change of the output capital ratio; the utilisation rate will begin to rise above thedesired level. This in turn may feed back and stimulate accumulation thus causing a

' This assumption is not critical to the argument. A simple alternative assumption could be g,=0, and thiswould cause no change in qualitative behaviour.

2 Equation (21) defines u as a function of;, u = cp(j) say, and (p<#)-» 1 for;->ya — 8 and <p(g)—u<>> 0 for;-> —8. Analogously, (23) also defines u as a function of;, u = y(g) say, and when A>0 we get v(g)->y/(/4 + (l —

>(ya-8) and vte)->0 for;— - 8 .

Finance, saving and accumulation 347

further rise in R. Indeed, if the original chance increase in R is maintained for a'prolonged period' then a further induced increase seems inevitable: firms will eventuallyrespond to a situation of less than desired capacity by raising investment. If, on the otherhand, the original rise in R is short-lived, and if accumulation does not respond to minorshort term deviations of utilisation from the desired level, then cumulative divergence willnot result. Although the warranted growth path is unstable in the face of major pertur-bations in the accumulation rate, it may not, therefore, have the knife-edge instabilitysometimes (wrongly) attributed to Harrodian theory.'

In order to derive more precise stability results, one would need to specify theshort-term properties of the accumulation function. The basic principle however isstraightforward. Strong and swift accelerator effects tend to produce instability whereas aweak and slow-acting accelerator may yield stability. Of particular interest in the presentcontext, however, is whether financial factors—not usually considered in Keynesiangrowth theory—may become a stabilising influence. The answer is no. As noted above[eq. (20)], the valuation ratio is positively related to the output capital ratio, and this wouldtend to reinforce the destabilising accelerator effects.

The analysis in this section seems to confirm both the instability of the warranted pathand the inequality of the warranted and natural growth rates. The empirical evidence foradvanced capitalist countries does, however, suggest that although there are pronouncedcyclical fluctuations in production and employment there is no monotonic divergencefrom an unstable warranted path. Furthermore, although unemployment has had a risingtrend over the last two decades one could still argue that long-run average growth rates arebroadly in line with natural growth rates. Can this evidence be reconciled with theKeynesian view? It is beyond the scope of the present paper to analyse this question indetail, but provided one adds a Marxian element to the analysis the answer is yes.

Changes in unemployment (in the reserve army of labour) may turn divergent move-ments away from the warranted growth path into cyclical fluctuations around the naturalrate. The homeostatic effects of movements in the reserve army of labour were emphasisedby Marx and they have been formalised by Goodwin (1967). Neither Marx's argumentnor Goodwin's formalisation takes any account of effective demand problems but theargument can be adapted and introduced into Keynesian models. See Skott (1989A,1989B) for a rigorous analysis of cyclical growth along these lines.

4. Alternative financial behaviour: type B firms

So far the financial behaviour of firms has been cast in terms of the parameters sp and N.It has been argued, however, by Wood (1975)2 that firms fix target values for theproportions of finance which are to be obtained from the three different sources. Anincrease in investment is thus directly associated with an increase in retained profits as wellas in the amount of new issues. Wood views the profit retention rate (Sp) as an exogenousparameter and uses the financial condition to establish a link between profitability andcapital accumulation. This pricing mechanism differs radically from the approach in diispaper where the mark-up factor is fixed.3 Type B films, however, come close to thebehaviour stipulated by Wood. Let

1 Harrod has strongly repudiated the knife-edge metaphor (see Harrod, 1973, ch. 3).J Other economists have expressed similar views on the connection between finance and the pricing and/or

retention decisions of firms (see e.g. Ball, 1973; Eichner, 1976; and Harcourt and Kenyon, 1976).3 Given the specification of demand—the level of demand depending on the price level—this seems the most

reasonable pricing assumption. In Wood's model the growth of demand is related to the price level.

348 P. Skott

B = sp(P-iAf)l(pI)(24)

ii = eNftl(pT)

and hence

(25)

Type B firms wish to maintain constant values of 0 and u. The parameters sp and ft remainthe proximate decision variables but the two parameters are continuously adjusted so as toensure the constancy of 8 and u. Does this alternative financial assumption affect theconclusions of the previous sections? The answer is, not much.

The analysis of type B firms is completely analogous to the case of type A firms. Thewarranted growth equations will, as before, have a unique solution, multiple solutions orno solution depending on the values of the parameters. There is only one noteworthychange. The likelihood of a stable warranted growth path has increased. The reason issimple. When type B firms decide to increase the rate of investment they simultaneouslyraise the retention rate, sp, and increase the amount of new issues, ft. This change in thefinancial parameters directly raises the average saving propensity for the economy andthus tends to stabilise the warranted path.

5. Exogenous money

The preceding section examined the implications of a change in the financial behaviour offirms. This section looks at a change in monetary regime. So far it has been assumed thatthe supply of money (of bank loans to firms) is perfectly elastic at some given rate ofinterest. This assumption is now reversed. Instead it is assumed that banks vary theinterest rate on loans to whatever extent is required in order to induce firms to expand theirtotal bank loans at some given growth rate, m. Individual firms still have unused overdraftfacilities with banks but the interest rate on these overdrafts is adjusted so as to make firmswant to increase the balance on these accounts at the given rate. Since firms hold no moneybalances themselves, this implies that the money stock of the household sector must growat the rate m.

The implications of this change are far more dramatic than those associated with thechange in the behaviour of firms. Substituting M = m into firms' financial constraint, (8),and assuming that a modified short-run equilibrium obtains (so that JI = y), we get

p 0 (26)

or, using (10) and (11),

/ = Yo [ ( r - ( l -y)pt) (ip + ai0) + P(l -y)w] (27)

The interpretation of (27) is as follows: current production is Vo and this level ofproduction is being sold at a price which yields the profit share y; firms wish to invest theamount / and in order to finance this, they need to set the financial parameters, sp and ft, atappropriate levels. Since m is given, this means that either j p or ft must accommodate. Inother words, / , sp and ft cannot be chosen independently, and the financing constraint onthe three variables is given by (27). Whereas in the Wicksell case firms (of type A) choseI, sp and ft and let dAf adjust, they are now, by assumption, induced to choose <LM = mM,and one of the other variables must play the accommodating role. It is important to note

Finance, saving and accumulation 349

that Yo and y are the existing level of output and the existing profit share; equation (27)describes a financial constraint between current variables and not a relation between somefuture expected variables.

Assume that firms have chosen some feasible combination of sp, 1$ and /. What will bethe modified short-run equilibrium growth rate of output? From (16) we get

p (28)

and combining (27) and (28) yields

Y = m (29)

In other words, firms' production decisions—the rate of growth of output—areindependent of the level of investment.

An alternative way to derive this result is directly from the demand for money equation,(11). By assumption we have

lfr=w+L=Y (30)

and logarithmic differentiation of (11) thus implies (29). The more circuitous route does,however, have an advantage: it shows how induced changes in firms' financial behaviourcan affect saving (and the size of the multiplier) and thereby make the exogeneity of mcompatible with autonomous investment decisions and equilibrium in the productmarket.

It should perhaps be noted that the success of 'constant m policies' in generating stablegrowth in output depends on several questionable assumptions. It has been assumed thatbanks can and will adjust interest rates to whatever extent is needed in order to inducefirms to increase their loans at the given rate. Furthermore, we have ignored the existenceof a range of monies and near-monies and paid no attention to financial innovation and tothe possibilities of substitution between existing assets.

It is outside the scope of this paper to analyse these questions in any detail. For presentpurposes the main point is simply that the overall monetary and financial regime is ofparamount importance and the polar cases (constant interest rates versus constant moneygrowth) bring this out very clearly.

6. Comparative staticsThe comparative statics of changes in some of the parameters are given in Table 1. Onlythe results for type A firms under Wicksell conditions are reported. The type B case is verysimilar as regards the comparative statics of changes in household parameters, and themonetarist case is extremely simple: the growth of output is fully determined by theexogenous rate of growth of the money stock.

Columns 1 and 2 of Table 1 show the orthodox short-run equilibrium effects of changesin the parameters. These columns are derived from equations (17) and (20), and are basedon the assumption that Y = Q. The average saving propensity is positively related to theparameters (a, y, sp, $ ) , and the equilibrium level of income therefore decreases if any oneof these parameters is increased. Because of this deflationary influence on output, theeffects on Tobin's q of increases in s^# or y are unambiguously negative. But in the caseof the household parameter, a, the negative effect of a fall in Y is counteracted by apositive 'valuation effect'. Total financial valuation, V, is the sum of two terms,V=$W+a(P—iM). For given values of R^and (P—iM) an increase in a would clearlyraise V, and this positive relation remains valid provided W and {P—iM) do not fall 'too

Tablet.

(1) (2) (3)<?[eq.(20)] ?[eq.(16)]

!

a N(y — (1P - ( J

p + u ^ ) ( l — Y) ' y ( l — Y) / [ (Y — (1 —y)PO2

JP (Y-(l-Y)PO -[P(l-Y) + u(Y-(l-Y)P')]/[(Y-(l-Y)PO(Sp + a^)2]///C - (Y-0 ~Y)PO/t(l ~Y)P1

fi U(Y-(1

Finance, saving and accumulation 351

much'. The change in output (and thereby in W and (P — iM) is determined by the changein the average propensity to save (the multiplier), and as indicated in column 1, the effecton the saving propensity of a rise in a depends on the amount of new issues, ft: nethousehold saving in securities is given by eNft = aft(P — iM). The rise in the savingpropensity (the fall in output) will thus be larger the higher is ft and the sign of dq/da isambiguous. It will be positive for small values of ft and negative for large values of ft.1

Finally, there is the somewhat surprising result that both output and the valuation ratioare positively related to p. This is because, by assumption, money holdings are constant inorthodox short-run equilibrium, and in equilibrium the rate of household saving out ofdistributed income is therefore independent of the value of p. Saving by firms, however,will depend on p. An increase in P will raise the proportion of bank finance and hence theshare of interest payments in total profits, and this leads to a reduction in retained earningsand thus stimulates demand. As in the case of a, there is both a saving effect and a valuationeffect on q following a change in p. But here they are both positive and the combined effectis thus unambiguous.

Column 3 is derived from equation (16) and it relates to modified short-run equilibriumwhere Y may differ from zero. The column shows the impact effect of parameter changeson the rate of growth of production: the level variables are predetermined and the preser-vation of product market equilibrium at the desired supply price implies that parameterchanges must be accommodated by changes in output growth. An increase in a, y, sp or ftwill, as one would expect, depress output growth. Changes in the parameter P, however,deserve comment.

If both the level of wage income and the stock of money are predetermined then a changein P cannot be introduced without violating equation (11), i.e. without leading to stockdisequilibrium. Conversely, if (11) is to hold at all times, then a change in P must beaccompanied by an instantaneous change in W, i.e. by Y = ± oo. Since sign Y = — signP weget the first entry for dYjdfy. Notice that a similar stock-flow problem does not arisefollowing an increase in a: an endogenous rise in the price of securities, e, causes arevaluation of the stock of securities without any need for new saving. In the case of a risein P no such automatic revaluation (fall in money wages and prices) enhances the real valueof the money stock.

Stock disequilibrium could, however, be avoided if P and M (or P, p and w) weresomehow changed simultaneously, and if this change satisfied the condition dM= Wdp(or H dP + PLdw = 0 if P and w are changed). On this assumption, one gets the secondentry for d Y/d$. The sign of this is ambiguous: in addition to the expansionary effect fromlower retained earnings, there will be a household saving effect, the saving effect beingproportional to the rate of growth of wage income.

Parameter changes also have long-run effects on the rate of utilisation and the warrantedgrowth rate. A rise in a or P reduces the cost of capital and thereby raises the share of pureprofits. The increase in pure profits in turn induces a decline in desired utilisation, but theeffect on warranted growth rates is ambiguous: the fall in utilisation tends to lower growthrates while an increased saving propensity has the opposite effect. Finally, the financialvariables of the firm sector have no influence on utilisation: the effect of a rise in either j p orft is simply to raise the saving propensity and thus the warranted growth rate.

' The impact effect on q of a rise in a, however, is unambiguously positive: the accommodating variable inmodified short-run equilibrium is the rate of growth of output, not the level of output. There is therefore noimmediate saving effect on the level of total profits and initially the price of securities bears the full burden ofadjustment.

352 P. Skott

8. ConclusionsWhat then can one say about the influence of saving and finance on accumulation? Severalconclusions emerge. First of all, the overall monetary regime is of the greatest importance.Under a monetarist regime, firms and households are, by assumption, induced to makesaving and finance decisions which ensure that output will grow at some given exogenousrate no matter what level of investment is decided. In the long run, the rate of accumu-lation will consequently also adapt to the exogenous money growth rate. Household andfirm parameters are left to determine only the desired utilisation rate. None of this issurprising but, in view of the reservations mentioned in Section 5, the Wicksell regimemay be of greater interest.

In the Wicksell case, household and firm decisions on finance and saving do influenceboth short-run output levels and long-term warranted growth rates. The basic principlewhich this model shares with simple flow models without any financial stocks is that a risein the average propensity to save will lower the short-run equilibrium level of productionand raise the warranted growth rate. The difference arises in the determination of theaverage propensity to save, s. In simple flow models, either s itself is typically taken as aparameter or s is defined as a weighted average of the propensities to save out of profits andwage income. In the present model, by contrast, s is determined by the interaction of fivehousehold and firm parameters, a, p, y, sp, # . '

The parameters a and P describe the behaviour of households, but the saving of house-holds out of distributed incomes is not determined by a and P alone; it is also influenced bythe amount of new issues and the growth of output (7? and i^). Furthermore, a change inthe household parameters has an important effect other than on saving: it also affects thefinancial valuation of firms (q). In fact, if $ = 0 then a change in a has only valuation effects;household saving will not be affected.

While an increase in saving propensities will depress short-run production and raise thewarranted growth rate, an increase in valuation has no immediate effects on short-runproduction but reduces the warranted rate (by raising the desired capital output ratio).The net effect of a rise in a or P therefore becomes non-positive with respect to short-runoutput (the saving effect) but ambiguous with respect to the warranted growth rate (bothsaving and valuation effects). Since a decline in the warranted growth rate is in factexpansionary when the warranted path is unstable, this implies that a rise in the 'savingparameters' may stimulate the economy: if the valuation effect on desired utilisation issufficiently strong then the net effect will be that utilisation rates are now above the desiredlevel. This will stimulate the rate of investment and increase both the accumulation rateand the rate of growth of production. A stimulating net effect is most likely following anincrease in a: if Tv' is small (which empirically it is in most countries) then the deflationarysaving effect will also be small.2

1 This implies that the multiplier becomes an endogenous variable. If for instance firms were to fix the rateof new issues so as to secure the immediate funding of all investment over and above some normal level, thenthe multiplier would vanish: saving would accommodate to investment without any changes in output ordistribution. New issues (and in an obvious extension of the model, bond issues by the public sector) thus havea 'crowding out' effect: they raise the saving propensity and, because of this, crowd out consumption andincome. A similar result has been obtained by Harcourt (1972, ch. 5). Harcourt assumes that prices are linkedto the level of investment and shows that this may give rise to a negative multiplier.

2 Even if the warranted rate is unaffected (or slightly increased) there may be an expansionary effect. Theimpact effect of a rise in a is to raise q and hence to lower u* (see p. 351, n. 1). If investment reacts quickly to thisdecline in u* below u, then actual accumulation rates may exceed the new warranted rate before utilisation rateshave fallen to their new short-run equilibrium level. A slow multiplier (a slow adjustment in output to changes indemand) and a fast accelerator (rapid adjustment of investment to deviations of actual utilisation from desiredutilisation) thus increase the likelihood of expansion following a rise in household saving parameters.

Finance, saving and accumulation 353

These results have implications for the debate on saving and finance in Keynesiantheory. An increase in the average saving propensity does not stimulate investment andoutput. On the contrary, the orthodox Keynesian view that increased saving propensitieswould depress output and thus future investment, is vindicated. But in a model withstocks of financial assets, a change in 'saving parameters' will affect both the savingpropensity and the valuation of existing assets. The valuation effect may in some casesdominate, and increased 'saving parameters' may thus stimulate investment and growth.In a model with financial stocks the desire to save will indeed influence the cost of finance,as claimed by Asimakopulos.

Changes in the firm parameters, 5p and fl, however, do not give rise to any valuationeffects.1 A rise in sp or $ will therefore unambiguously deflate short-run production andraise the warranted growth rate, thus tending to depress investment levels as well. If onewants to stimulate the economy by raising the desire to save, it is therefore important tochoose the right target parameters. One should also, of course, make sure that conditionsare such that the valuation effect is likely to dominate the saving effect, and even if theseconditions are satisfied, one should not expect the expansionary effects to show upimmediately: it is unlikely that the rate of investment will respond quickly to a rise infinancial valuation in a situation where saving effects reduce the growth in output. As ageneral policy prescription, the suggestion that greater incentives to save may be used tostimulate the economy thus looks very dubious.

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