Kalecki S Long-Run Theory of Effective Demand

Modern Economists

By

Corrado Bevilacqua

Michal kalecki

i libri di laprimaradice.myblog.it

KALECKI’S LONG-RUN THEORY OF EFFECTIVE DEMAND:

THE TREND AND Business Cycles

In 1933, when constructing a macro-dynamic business cycle model, Kalecki’s purpose was to explain observed cycles with a macroeconomic theory capable of mathematical expression, leading to a dynamical system whose solutions are endogenous, deterministic cycles of constant amplitude. In substance, the demonstration of the intrinsic instability of capitalist economy was at stake. With this purpose in mind, using a linear mixed difference and differential equation, Kalecki tried to show at the 1933 Leyden meeting of the Econometric Society that this aim had been reached, showing in particular that his system gave rise to a cyclical solution of constant amplitude for a special value of the parameters. But,

“Alas, Frisch was there to point out that since the Greeks it has been accepted that one can never say an empirical quantity is exactly equal to a precise number. Given his aim, this was a deadly blow to Kalecki […]”. (Goodwin 1989, in Sebastiani 1989, pp. 249-250)

Owing to the remarks he received, afterwards Kalecki temporarily accepted Frisch’s Swinging System approach whereby the economy has a natural tendency to reach a stationary equilibrium and cycles occur due to exogenous shocks. Pushing momentarily into the background the demonstration of the intrinsic instability of capitalist economies, he thus centred his efforts on the explanation outlined in the conclusion of its 1934 article “Three Systems” (Kalecki 1934 (1990a), p.219). In that paper, taking into account a gestation period of investment, Kalecki described cycles as a succession of temporary equilibrium, each one characterised by both a given level of investment expenditures and capital stock; resulting respectively from decisions taken in the past. The case corresponding to un-damped oscillations appears thus as a special configuration in which the economy, passing from one quasi-equilibrium to another, never reaches a stationary equilibrium (two equilibrium being then crucial: the quasi-equilibrium “high” and the quasi-equilibrium “low”, respectively perturbed by variations in the capital stock).

Somewhat later, still unsatisfied with his previous model, Kalecki outlined a new business cycle theory, whose main innovation found its root in a critic he had addressed to Keynes (Kalecki (1937 [1990]). In this model, Kalecki aimed at generalising Keynes’s analysis of investment to situation in which 1) long term expectations are not exogenous but endogenous and related to the current situation and 2) returns on capital equipment are not decreasing but constant. Regarding point 1), Kalecki suggested capturing the sensitivity of long term expectations to the current situation by introducing a non linear function of investment decisions aiming at showing that these are affected from waves of optimism and pessimism occurring at particular moment of the cycle. Regarding point 2) Kalecki introduced one of his most important considerations, namely the principle of increasing risk, on which he built a new analysis of the decision to invest.

In 1943, however, he developed a new model and introduced two important innovations to his previous version. In the first place, he followed a remark of Kaldor who, relying on Kalecki’s 1939 model[1], showed that what was logically required for constructing a mathematically robust endogenous explanation of fluctuations is that the stationary equilibrium must be unstable, so that the system will never reach it. Thus, abandoning the reference to random shocks, he developed a new explanation fundamentally endogenous in which fluctuations results mainly from waves of optimism and pessimism. In the second place, he enlarged the scope of his model, with the aim of formulating a dynamical system whose solution would encompass both the cycle and the long run development of the capitalist economy.

However, he came again, in a new form, to deal with the factors explaining the cycle and long-term growth in the Theory of Economic Dynamics Kalecki (1954[1991]). In that book he admitted the damped nature of fluctuations and explained the constant amplitude of cycle by shocks; however, apart from this, the 1954 version of the cycle is not radically different from the 1943 one. Finally, in 1968, in the last version of his theory, he introduced some important modifications, related to the influence of results obtained by firms in the recent past, and to the impact of technical progress on recent investors, on investment decisions.

In this presentation, we will attempt to describe the different steps in Kalecki’s works on growth and cycles in the capitalist economy. In the text we will not deal extensively with his last attempt of 1968, because in the Appendix we reproduce Kalecki’s lectures on his 1968 paper, based on the notes taken by one of us (JL) who had the opportunity to attend these lectures.

Kalecki’s 1933 model

Kalecki’s business cycle theory can be considered as one of the first results, together with Frisch’s 1933 “Swinging System”, of a mathematical theory of the business cycle. Each one combines two essential elements. A set of carefully chosen and empirically observable facts is formalized, and then a soluble mathematical model is deduced. As Tinbergen emphasized: “the exact form in which it is presented [Kalecki’s theory] creates the possibility of a clear and fruitful discussion” (Tinbergen 1935, p. 270). Furthermore, Kalecki presented his business cycle theory in the form of a linear mixed difference and differential equation so that the properties of his approach become obvious.

The model concerns a two-class society in which income distribution and profitability variables are of primary importance. National income is equal to wages plus profits; spending by capitalists depends on profits, whereas workers’s spending is equal to total wages.

As regards consumption, capitalists are assumed to spend their profits either on consumption or investment goods. Let stand for total real income of capitalists, total employment, the real wage. Kalecki uses the following relations:

Where and are respectively real purchases of consumer goods by capitalists and by workers. The consumption function of capitalist is very similar to the Keynesian consumption function, with and , the main difference being that it applies only to capitalists and not to all consumers.

There are two main determinants of investment: the gross rate of profitand the money rate of interest denoted by . However, such variables, in Kalecki’s opinion, do not influence the investment orders but rather its level relative to the capital stock, that is the ratio : when and increase in the same proportion, so that the ratio remains unchanged, probably rises (Kalecki 1933 (1990a), p. 74). Thus we have the equation:

In the absence of external shocks and except for situations of ‘financial panic’, the money rate of interest usually varies according to the general business conditions, which are represented by . Being thus directly related to the current profitability of the equipment in use, the money rate is discarded, and consequently is a function of only. In a linear form, the investment function can be written as follows:

(1)

denotes gross profits (inclusive of depreciation), investment orders,, capital stock and and two parameters assumed to remain constant.

The cyclical nature of the solution of this model is due primarily to the gestation period of investment, from which it results two lags: one between investment orders and actual expenditures of investment and another between investment orders and the deliveries of equipment. Three stages must thus be distinguish for each investment: investment orders, the production of investment goods, , and their deliveries, .

Let be the average gestation period of investment so that deliveries of equipment at time are equal to orders of investment at time . We thus have:

(2)

The relationship between investment orders and investment outlays is more complicated. Since each order requires a period of time to be filled, and assuming that the construction of the capital goods proceeds at an even pace (that is, of each order is executed per unit of time), it follows that the production of capital goods is equal to:

(3)

This equation means that the output of capital goods at time is equal to an average – expressed in continuous terms – of the orders placed in the interval .

Finally, if we call the capital stock, its first derivative with respect to time (K’(t)) is its net increment, so that:

(4)

Where indicates physical depreciation. Kalecki assumes that in the period under consideration is a constant.

The system can be closed by adding the equilibrium condition of the goods market. In equilibrium, aggregate expenses are equal to aggregate income:

When workers´s consumption is equal to the real wage bill, we obtain Kalecki’s profit equation showing gross profits are equal to capitalists’ expenditures.

As Kalecki remarked:

“Thus capitalists, as a whole, determine their own profits by the extent of their investment and personal consumption. In a way they are masters of their fate; but how they master it is determined by objective factors, so that fluctuations of profits appear after all to be unavoidable” (Kalecki 1933 (1990a), p. 79-80)

By replacing by in the investment function (equation (1)), Kalecki thus obtains a model of four equations and for unknowns. Equations (1), (2), (3) and (4) allow determining the four endogenous variables , the exogenous variables being , and .

As we pointed out, investment decisions cause lagged relations in two directions: If investment is rising this entails an increase in both profits and in capital; higher investment will raise demand and profits, and stimulate higher investment decisions; but the rising stock of capital will tend to reduce the profit rate and negatively affect investment decisions. It is the interplay of these two opposite forces that creates the cyclical movement. Sooner or later the growth rate of one will overtake the other, and a turning point will be reached. In such a way the system will self-generate four phases of the cyclical movements: boom will give rise to recession, recession to depression, depression to recovery, and recovery to boom. The expansion of the productive apparatus hampers the upward cumulative movement, bringing it to an end and to the eventual slump. Expansion is converted into contraction, which assumes a cumulative character by a process inverse to that of cumulative expansionary movement. Investments exert a retarding effect when positive or an accelerating effect when negative. This means that, in a trendless economy, negative investments extricate the economy from the slump, just as the accretion of capital stock is responsible for the turning point in the boom. The growth of national wealth contains the seeds of retardation of the growth rate of economic activity. During a considerable part of the cycle, the additional wealth proves to be merely potential in character, as the accumulated capital is substantially underutilized. It becomes productive only in the successive upsurge. Disinvestment, or decapitalisation of national wealth, spurs prosperity, breeds forces that put an end to the shrinkage of capital, and stimulates the upswing; but, again, the expansion of capital contains the seeds of depression.

Reducing his system to a linear mixed difference and differencal equation, Kalecki tried to express formally this business cycle explanation by suggesting a solution based on the specification of parameters. As it is now well known, a linear mixed difference and differential equation can give rise to any of the three following types of oscillatory behaviour, depending on the value of the parameters chosen in the equation of the system (the coefficient of the first order term):

a) For a negative coefficient, the amplitude of fluctuation may grow ceaselessly, thus being unstable.

b) For positive coefficient, it may be stable, with ever-decreasing amplitude,

c) If equal to zero, its behaviour may lie exactly in between the other two so that it neither grows nor decreases in violence.

As Goodwin remarked:

“Kalecki very sensibly chose the value zero thus avoiding the dilemma, since his aim, in the Marxian tradition, was to explain how and why capitalism was, by its very nature, bound to oscillate. His solution combined theoretical necessity with practical convenience since it determined the one parameter for which he had no evidence”. (Goodwin 1989, in Sebastiani 1989, p. 249)

Indeed, Kalecki’s purpose was to construct a system whose solution would have been endogenous, deterministic cycles of constant amplitude[2]. Therefore, according to him, the demonstration of the intrinsic instability of economy was at stake[3]. This feature of Kalecki’s approach becomes all the more evident when compared to Frisch’s solution. Contrary to Kalecki, Frisch accepts the idea that economy has a natural tendency to reach its equilibrium state, in other words, that the system is intrinsically stable. From this point of view, if the cycles observed are undamped, this is due to erratic shocks. Referring to Kalecki’s presentation in Leyden Frisch wrote:

“The imposition of the condition that the solution shall be undamped is in my opinion not well founded. It is more correct, I think, to be prepared to accept any damping which the empirically determined constants entail, and then explain the maintenance of the swings by erratic shocks”. (Frisch 1935, in Kalecki 1990: 447)

Thus, when Frisch criticized Kalecki’s solution, it was in reality Kalecki’s approach to the dynamics of capitalist economy he criticized. This did not escape Kalecki and from 1934 onwards he abandoned his original approach of an undamped system, and relied on shocks as one of the factors determining the cycles. In other words, since this date he thus changed the course of his research and decided to precise the mechanisms at works in his model, analysing especially the mechanisms which made the economy converge to a temporary equilibrium.

Kalecki tried however to improve his analysis, especially by dealing more precisely with expectations. From 1936 onwards Keynes exerted a great influence on him; but if Keynes seems to have persuaded Kalecki to treat the expectation issue more thoroughly, this does not mean that he adopted entirely Keynes´s outlook. Indeed, Kalecki’s Essays written in 1939 are clearly an attempt to “generalize” Keynes theory. We now discuss Kalecki’s new version of his business cycle theory as developed in this book.