TOWARDS A DYNAMIC ECONOMICS

THE ECONOMIC RECORD DECEMBER, 1948

TOWARDS A DYNAMIC ECONOMICS

I Smith, Ricardo, Marx and Mill were all primarily interested in

analysing the factors of economic progress. It is rather curious that the theory of secular trena’ should have received so little attention from later generations of economists. True, there have been a few distinguished works in the field, notably those by Schumpeter, Sweezy, Lundberg, Clark and Ayres, Hansen’s ‘stagnation’ thesis is essentially a theory of trend although imperfectly and incompletely formulated ; Kalecki has presented an elegant extension of his theory of fluctuations to an analysis of trend; and Domar has made interesting sug- gestions about economic growth.2 Yet none of these works provides a completely satisfactory theory of economic development, nor even a solid foundation on which such a theory could be built.

What, ultimately, would a complete t.heory of economic development do f o r us? It might enable us to forecast future trends; but more important, i t would tell us what sorts of policy were needed to maintain as rapid a rate of increase in income per capita as is compatible with stability and with time preference. It is obvious enough that the factors determining the rate of increase in per capita income are the rate of technological progress, the rate of discovery of new resources, the rate of capital accumulation, trends in the efficiency of allocation of resources, and trends in the level of, unemployment. There is not much that can be done by economic policy alone to accelerate or maintain the rate of technological progress or the rate of discovery of new resources. The chief policy questions are, therefore, how to assure an optimum rate of capital accumulation and how to eliminate secular causes of unemployment and misallocation of resources. If progress is to be consistent with stability, secular causes of inflation must be eliminated as well. Thus no dynamic

1. Tewards a Dunamic Economics. By R. F. Hsrrod (MacmiUaa & Ca Ltd.. 1948). Pp. ix + 169. 7/6 ste.

2. Joseph Schumpeter. Business Cvdcs. New York. 1939, and The T h e m of Economic Vwelopment, Cambridne. 1927; Paul Sweezy. The Theorv of Capitalist Development. New York. 1942: Eric Lundberp. Studies in the Theom of Economic Ezpansim, London, 1937: Colin Clark. The Conditions of Economic Progress, London, 1941: C. E. A m , The T h e m of Ecmwmic Progress. Chapel Hill. 1944: Alvin Hansen. FuU Recateru OT SecuLor Stagnation. New York.. 1938. and Fiscal Policv and B u h e s s Cuelea. New York. 1941; Benjamin Hipgins. Concepts and Criteria of Secular Stagnation,’ in Income. Emploument, and Pubfic Policn:. Essays in Honour of Alvin Hamen, New York. 1948 : Michael Kalecki. Studies m Economic Dynamics. London, 1943 ; Evsw Domar, ‘Expan- sion and Ernplyment.’ American Economic Review. March 1947. and ‘Investment, Losses. and Monopolies in Income. Employment, and Public Polioti. op. cit. See also B. S. Keirstead. The Theory o f ’ E c m i o Change. scheduled for early publication by Macmillan.

173 A

174 THE ECONOMIC RECORD DEC.

theory is adequate that does not either demonstrate that there are no secular causes of unemployment, misallocation of resources, and inflation, or isolate the secular causes of these unwanted phenomena and suggest means of dealing with them.

Evaluated on this criterion, few of the existing theories of economic development stand up well. To take just one example, Schumpeter ’s theory really explains only why capitalistic economic development will no; take the form of smooth growth, but rather of fluctuations around a rising trend. The growth itself is hardly explained at all ; it apparently depends upon population increase, new resources, and-above a l l - o n a swelling stream of innovations, which depends in turn upon a growing supply of ‘entrepreneurs,’ the ‘new men’ who will found ‘new firms’ and construct ‘new plant and equipment.’ Why should the supply of new men grow, o r why should it ever stop growing? Here Schumpeter’s theory borders on the metaphysical; certainly it becomes a good deal less systematic than his explanation of the cyclical fluctuations that take place around the trend. He does, of course, suggest a theory of stagnation; capi- talism, by its very successes, breeds a social atmosphere hostile to it, and antipathetic to the nurture of new men. Maybe; but Schum- peter can hardly be said to have furnished convincing proof, either analytical or empirical, that s w h must be the case. Nor has he proved that in the stage of most vigorous capitalistic growth, the stream of new men must be a growing one. The other extant theories have similar inadequacies.

Another weakness of the rather special theories of economic development that have been presented thus f a r is that they do not link up satisfactorily with the body of equilibrium theory. Today, theories of economic development are as much on the periphery of the main corpus of received doctrine as theories of economic fluctua- tion were twenty years ago.

For these reasons Mr. Harrod’s essay on Towards a Dynamic Economics is a most welcome addition to the literature. In the first place, his theory has the main attributes of a satisfactory dynamics. Harrod concentrates upon the explanation of secular trends, and --quite properly, in this reviewer’s estimation-insists that it is precisely this explanation of trends that is the distinguishing character- istic of a truly dynamic economics. Comparative statics, he argues, are still statics; it takes more than imperfect foresight, o r imperfect knowledge, or mere change, o r ‘presence of expectations, o r lags and frictions, or ‘dating’ of variables, to take us into the realm of economic dynamics. Even trade cycle theory is not dynamic if it merely explains fluctuations around a constant trend. Only a theory explaining secular changes in the volume of output has the right to be called dynamic.

1948 TOWARDS A DYNAMIC ECONOMICS 175

In the second place, Harrod’s theory is directed towards an explanation of the secular causes of unemployment and inflation, and of the factors determining the optimum and the actual rate of capital accumulation. Of the major components of a complete theory of economic development, only the secular causes of misallocation of resources are entirely neglected by MI. Harrod.

In the third place, Harrod’s theory, while clearly distinct from theories of eqnilibrium or of comparative statics, is nevertheless related to them, and makes use of those concepts and tools of equilibrium theory and comparative statics that are useful in analysing secular trends. Accordingly, his work provides a foundation upon which i t should ultimately be possible to build, brick by brick, a quite imposing structure of dynamic analysis.

Mr. Harrod considers the building of such a structure the major task facing economists today: ‘The idea which underlies these lec- tures,’ he writes, ‘is that sooner or later we shall be faced once more with the problem of stagnation, and that i t is to this problem that economists should devote their main attention’ (p. v). Here again the reviewer finds himself in enthusiastic agreement. The theory of equilibrium of the household and firm is still, heaven knows, a very messy piece of apparatus ; yet it stands up amazingly well, and serves quite adequately both to explain what happens in the market and t o provide a basis for policy recommendations. The theory of economic fluctuations, with its new econometric design, has become the most impressive wing of the whole structure of economic theory. If a smooth-working economy required only the elimination of fluctuations around a trend of full-emplopent national income, the problem would certainly be more political than economic. But if, as Harrod believes, we are faced also with persistent tendencies towards unemployment or inflation as well, the policy problem is obviously much more complicated. Accordingly, it behoves us to find out whether and how such persistent deflationary o r inflationary gaps are likely to arise, and how best they can be eliminated o r oEset.

Harrod, on the basis of his analysis, concludes that advanced countries will soon face the problem of a chronic deflationary gap, and that under-developed (‘ capital-scarcity’ countries) will continue to be handicapped by a chronic inflationary gap, unless appropriate policies are pursued. True, the United Kingdom wi l l be faced for the balance of the transition period with a problem of under- rather than over-saving, and if the secular downward drift of the propensity to save continues, it may be a long time before chronic unemployment becomes the major economic problem in that country. ‘But the United States,’ Harrod thinks, ‘is not likely to be exempt from the problem of chronic depression’ (p. vi). And what happens in the United

176 T H E ECONOMIC RECORD DEC. States must affect the rest of the world. It is therefore high time, in Harrod’s opinion, for economists to turn their attention once again to problems of chronic and increasing under-employment.

I1 This review will concentrate upon the systematic theoretical

analysis in Harrod’s essay. The book also .contains some useful discussion of contra-cyclical policy, and some fascinating pronounce- ments on social philosophy. However, these parts of the essay are readily understandable, and do not provide a foundation for future system-building to the same extent that the central analytical chapters do. Moreover, these central chapters are frightfully Mcult-not for the mathematics, or complicated diagrams, or long-winded discussion they contain, but precisely because all such aids are left out. There are whole paragraphs between the lines that the reader must fill in for himself; and in many cases it is no easy task to write a paragraph elaborating the argument of one line and come out with something that fits Harrod’s nest line. Accordingly, the reviewer felt that it might be useful, both to those who want to read the book and to those who want only to know its main conclusions, to present in summary form the results of his own struggles with Harrod’s cryptography, as well as to offer a few critical remarks along the way.

Harrod’s first chapter is devoted to a defence of his definition of ‘dynamics,’ and to laying down aafew fundamental concepts. In contrast to the classical theory, in which economic development is treated as a race between technological progress and capital accumulation on the one hand, and diminishing returns to a growing population applied to a h e d supply of land on the other, and in which population growth is a dependent variable mutually determined with profits, investment, income and so forth, Harrod discards diminishing returns’ from land as a ‘primary determinant,’ and considers both the rate of population growth and the rate of technological progress as independent variables in advanced countries. The three ‘fundamental elements’ in his system are: (1) manpower, (2) output per head, (3) quantity of capital available. The second of these presumably breaks down into (a ) Level of technique, (b) Supplies of known resources; but Harrod discusses changes in output per head solely in terms of ‘inventions.’

A ‘neutral’ stream of inventions is one that leaves the ratio of required capital to output (‘ capital coefficient ’) unchanged. A ‘ capital-saving ’ stream of inventions would reduce the capital coefficient, a ‘labour-saving’ stream of inventions would increase it. Thus ‘labour-saving ’ inventions are defined as capital-absorbing inventions. Surely an invention could reduce the ratio of labour to


output, without raising the ratio of capital to output? This definition also raises the question, which pops up periodically in the course of Harrod’s analysis, as to whether he really means inventions when he uses the word, o r whether he means innovations. An invention may be capital-saving once in place, but the innovation based on it may nevertheless be capital absorbing during the gestation period. What is needed for a growing offset to savings is not a stream of inventions that is capital absorbing in the engineering sense, but a stream of innovations that is capital absorbing in the economic sense.3 Harrod, unfortunately, fails to make this important distinction. He seems to be talking mainly about inventions, which, he says, may very well be more or less neutral in reality (p. 28) ; but a t times his argu- ments make sense only if cast in terms of innovations.

‘ Capital requirements’ are the proportion of income that must be saved and invested to maintain a given rate of increase in income, with a given rate and type of technological progress, and a given rate of population growth. A simplifying assumption that underlies the discussion of capital requirements, which Mr. Harrod does not make explicit, is that the labour force and the body of consumers grow in the same proportion; that is, that the ratio of labour force to population and of consuming units to population does not change. Only then would it be true, fo r example, that capital requirements with no technological advance and no change in interest rates would equal ‘the increase of populatioh in a period regarded as a fraction of the total income multiplied by the capital coefficient’ (p. 22).

More generally, his concept of capital requirements (C,) could be translated as follows. Let I, be required net savings and investment, Y be national income, and p ( fo r period of investment) be the

‘capital coefficient.’ Then I, = -. p , and C,= I n Chapter 2 Harrod proceeds to analyse trends in (net) savings;

f o r the relation of trends in net savings to trends in new capital requirements is obviously of major importance in determining whether or not there wi l l be a steady growth. He distinguishes three major sources of saving: (1) Individual saving to satisfy a person’s own needs during his own lifetime (which he calls ‘hump’ saijng) ; ( 2 ) Individual saving for the purpose of enlarging an estate to be passed on to heirs (which we may call ‘inheritance’ saving) ; ( 3 ) Saving

A P I Y A Y ’

3. Cf. B. Hippins, og. n’t. 4. If ‘P’ is population and ‘L’ is level of technique. ‘:’ ia time and ‘R’ b quantity of

capital required for a given level of output. then

Then, ignoring cms-derivativei. which would in any caee be very a d ,

R = R(P.L) . where P = P ( t ) and L = L ( t ) .

dR SR dp SR dL

dt SP dt 6L dt 17 = - = - . - + - . ? ’

‘L.’ is here defined in terms of output per -pita.

178 THE ECONOMIC KECORD DEC. by business firms (which he calls ‘ corporate’ saving). Harrod believes that in a stationary state, with neither population growth nor technological progress (nor, although Harrod fails to distin,pish this factor, discoveries of new supplies of natural resources) ‘hump’ savings should be zero for the economy as a whole; saving of the young wiU be just ofbet by the dis-saving of the aged. It is worth noting, however, that ‘hump’ savings would be zero only if tastes regarding the time-pattern of enjopmenta throughout a lifetime remained unchanged from generation to generation. Harrod feels less certain about ‘inheritance’ saving, but thinks it most likely that they will be positive, although small, and diminishing through time. Corporate saving, which is motivated primarily by the desire of .entrepreneurs to expand their businesses without forfeiting a controlling interest o r unduly enlarging fixed charges, would tend towards zero in a stationary society. If ‘inheritance’ saving is positive, since there would be no demand for saving in a stationary economy a t a constant rate of interest, there would be a chronic tendency for savings to exceed investment, and ‘it would be necessary to have a falling rate of interest to give employment to the savings volunteered’ (p. 47).

Even then, the falling interest rate would absorb savings only to the extent that it led to more roundabout methods of production; and the falling interest and longer investment periods would probably induce firms to save more themselves, leading to a further decline in the interest rate, and so on. It is hard to say what the effect of falling interest would be on ‘inheritance ’ saving ; but Harrod concludes that ‘hump’ saving is an increasing function of the rate of interest. This conclusion is derived from putting ‘reasonable’ values into his savings equation,

1 = cr [I - e (1 - m)] in which ‘C1’ is consumption in year one, ‘ C r ’ is consumption in a later year r, ‘ 6 ’ is the average elasticity of the income utility curve over the relevant range, T is the reciprocal of the rate of time- preference, and R the number of pounds to which El accumulates a t the end of the year a t the current rate of interest.

It is a pity that Mr. Harrod could not have provided his readers with his computations, in a footnote or Appendix; but there is little reason to suspect his conclusion. Indeed, if one considers savings as demand for future income and translates the interest rate into a price of future income in terms of present income, i t becomes fairly obvious that savings out of a given income must vary directly with the interest rate. The conditions for a rising demand curve are the same for ‘future income’ as for any other commodity: the commodity must be one on which a large &are of income is spent, and it must be highly


competitive with but inferior to some other commodity. These conditions are simply not fulfilled for most savers. The effective increase in present income through having to pay a lower price for future income must be insignificant for most people; and while future income might be inferior to present income, it can hardly be considered highly competitive with it.

In an economy with a growing population and no technological progress, capital requirements will increase proportionately to the population. So also, Harrod argues, will ‘hump’ savings and ‘corporate’ savings. Consequently, if there is ‘inheritance’ saving to begin with, and all capital requirements are to be met, ‘inheritance’ saving must also grow proportionately t o income; that is, it must grow in total volume enough to keep the average per capita inheritance constant. Of course, total savings may tend to grow faster than capital requirements, leading to a condition of chronic excess savings and a need for falling interest rates, even in an economy with a growing population; but the need for a falling interest rate is clearly much greater in a stationary state than in one with a growing population.

In an economy with technological progress as well, it is necessary to ask what is the effect on saving of an increase in per capita output. The effect on elasticity of income utility is, unfortunately, unpredictable. ‘On the other hand,’ Harrod writes, in a mature economy ‘there seems to be a presumption that time preference mill fall (that T will increase). As income rises our consumption is less dominated by basic physical need and becomes more amenable t o rational planning. . . . A strong time-preference is indicative of a low degree of civilization’ (p. 53). Perhaps; but how then does Harrod explain the observed secular tendency for the propensity to save to fa l l i True, the observed trend is a trend of ez post savings, which are necessarily equal to investment; and the observed trend may be causally explained better in terms of a declining ratio of investmemt to income than in terms of a declining ez ante propensity to save. Also, in the period for which data are available, there has been some tendency fo r interest rates to fall, and the fall in propensity to save may be a reflection of the drop in interest rates. However, this reviewer, at least, would have been happier if Mr. Harrod had linked his statements about falling rates of time-preference on pp. 53-55 with his statements about the actual trend of the propensity to save on p. vi.

Harrod contends that ‘hump’ savings are likely to grow faster than income when income per capita is rising. Here we run into the same sort of problem. Harrod’s contention presumably means that the trend of the average propensity to save for ‘hump’ purposes will

180 THE ECONOMIC RECORD DEC. be a rising one. Empirically, it is virtually impossible to separate ‘hump’ saving from other kinds of saving, as well as to measure e x ante savings as a whole. What we know is that historically, neither the average nor the marginal propensity to save shows any significant long run change, while in any one year families with high incomes have considerably higher average propensities to save, and somewhat higher marginal propensities to save, than families with low incomes. From this combination of facts it has been deduced that there is a downward secular drift of the propensity to save schedule, which just offsets the secular rise in incomes, leaving the actual ratio of savings to income ~ n c h a n g e d . ~ There is also some evidence that the downward drift of the propensity to save schedule may be the product of cycles of increasing amplitude. Savings seem to follow income up in the downswing, but to shrink in the downswing as families endeavour to maintain their prosperity standards of living in the face of falling incomes. As higher levels of national income are reached, more families will be able to meet depressions by dis-saving.6 Might not this downward drift in the savings function d e c t ‘hump’ savings too, and so prevent them from rising faster than income in the long run? In any case, one wishes that Harrod had been more careful to distinguish among the volume of savings, the propensity to save function, the average propensity to save, and the marginal propensity to save, in his ar,auments.

Regarding ‘inheritance’ saving, Harrod considers the evidence inconclusive, but feels that the increasing capacity for looking ahead in advanced societies would apply here too. Since corporate saving is unlikely to increase less rapidly than income, introduction of ‘neutral ’ inventions into the argument increases, rather than decreases, the possibility of chronic excess-savings. The existence of a large dead-weight national debt, which historically a t least is a feature of mature economies, also adds to the possibility of excess savings, so long as capital accumulation bears some more or less constant relationship to the existing supply of assets.

The second chapter concludes with some remarks about the possibility of a continuously falling interest rate, from the viewpoint of the securities market. Harrod points out, quite rightly, that it is the rate of interest implicit in share prices that is most relevant to decisions regarding new investment, and that ‘ordinary shares issued by good companies’ are not dissimilar to undated government stock. How could the market deal with such things if it came to expect a continuously falling rate of interest 4 F o r ‘the value of stock having no redemption date becomes indeterminate unless we put a

5. cf. Paul Samuelnon. ’F‘ull.Ernployment after the War.’ in Postwar E c o n a i c p70&,ma

6. Cf. James S. Duesenberry. Income-Consumption Relations and their Implications; (d. S . E. Harris). New York. E43. P. 33.

in jncoms, Employment. and Public Policu, o P . c i t .


term to the fall in the rate of interest’ (p. 60) ; and even a decline expected to end in 20 or 30 years would produce awkward anomalies in the market. ‘Dynamic theory strives after the concept of a steadily falling rate of interest, but I do not think that market conditions have been envisaged in which this could become a reality’ (p. 62).

I11 I n chapter three, which is the heart of the book, Harrod presents

a revised version of the ‘fundamental equations’ developed in his Economic Journal article of March 1939, and uses them to derive some extremely interesting ‘ dynamic theorems.’ The basic equation is GC = s, where ‘G ’ is the growth during a unit of time ( n Y / Y ) ; ‘C’ is net capital accumulation in the period (including goods in process and stocks), divided by the increase in output in the period

( I / a Y ) ; and ‘s’ is the average propensity to save, ?.7 Thus the

equation is really a restatement of the truism that ex pos t savings equals ex pos t investment; it could be written-

P

Ahp I S

I S Y Y

or I = S.

-.- = - P A P Y

or -- _ -

Harrod’s second fundamental equation, G,C, = s, expresses the equilibrium conditions for a steady advance. ‘Gw, ’ the ‘warranted rate of growth,’ is the value of AY/Y that barely satisfies entrepreneurs; ‘Cr,’ the ‘capital.requirements,’ is the value of I /Y that is needed t o sustain the warranted rate of growth.8 It mill be noted that ‘s’ is the same in both equations. Thus in dynamic equilibrium (stable value of AY/Y), G,C, = GC; the actual, or ez post value of I/Y, equals the equilibrium value, which is a subjective pheno- menon. Moreover, ‘G ’ must equal ‘Gm’ and ‘C’ must equal ‘Cr.’ For if ‘G’ exceeds ‘G,,’ then ‘ C ’ will be below ‘Cr’; that is, entrepreneurs will consider the amount of capital accumulation inadequate to sustain the increase in total output, and wil l increase their orders for capital goods (and conversely). But then ‘G ’ will depart still further from ‘Gw’ in the next period, and a cumulative movement away from equilibrium will set in. Thus, ‘Around the line of advance

7. These imbol s are used in the *Me: ‘Y’ u national income. ‘I’ in net investment. and ‘s’ is net savinFs. Since H a d ha3 P m m p t e d ‘C’ for another use, we s h d denote consumption by ‘Cn.

8. If inventions are ‘neutral.’ ‘Cr’ d l also be the new capital required to austain the increaae in consumption that cOMUmen Want. aa e, result of the increaae in their incomes during the period.

182 THE ECONOMIC RECORD DEC. which, if adhered to, would alone give satisfaction, centrifugal forces are a t work, causing the system to depart further and further from the required line of advance’ (p. 86) .

There are two possible interpretations of Harrod’s argument that if ‘G’ esceeds ‘Gw,’ ‘C’ must be below ‘C,.,’ and vice vema. If G,C, = GC = s by assumption, then the proposition follows by mere arithmetic. Harrod’s presentation, however, suggests that he thinks ‘G,C,’ must equal ‘GC’ for economic and definitional reasons, in much the same way that ez post savings must equal ez post investment. It is hard to see that such is the case. I t is clear enough that

I ‘ G ’ and ‘ C ’ must vary inversely j with a given-, the bigger G = Y/Y, Y the bigger Y, and thus the lower -or ‘C.’ B u t why should the

equilibrium ratio of (ez p o s t ) savings and investment to income (i.e. the ratio that satisfies entrepreneurs, or G,C. = equilibrium I = S

) be continuously equal to the actual ratio of savings and Y

I Y

I = S Y investment to income (GC, or actual -----) ?

Harrod’s main ar-aument does not depend upon the equality of ‘GC’ and ‘G,C,’ anyhow. It depends rather on the acceleration principle (or better, on the ‘relation’). For if ‘G’ exceeds ‘Gm,’ what this really means is that the rate of increase in consumer spending is greater than is necessary t o call forth the current rate of investment, and consequently investment will increase. By definition, if the rate of investment is below the equilibrium level, ‘Cr’ is below ‘C.’ Such a situation would be inconsistent with an excess of GC

(actual - = -) over G , C, (equilibrium - = - ) , since investment

cannot be simultaneously above and below the equilibrium level j but it would be quite consistent with a n excesa of G,C, over GC. That is, (C - C,) may esceed ( G , - G) ; entrepreneurs may consider actual investment low, not on ly relative to the actual rate of increase in consumer spending, but also relative to the level of income. In this case, there would be a double incentive to increase investment in the next period. The movement away from equilibrium when G > C, and in addition GC < G,C,, will be greater than if G > G, but GC = G,C,

Harrod anticipates the criticism that his formulation gives too much weight to the acceleration principle, and suggests that the criticism could be met by rewriting the first equation GC = s - k , where ‘k’ is investment not due to the current increase in orders for output. It is not quite clear how much investment is meant to go

I S I S P Y ’ Y Y


into ‘k”and how much into ‘(2.’ ‘ C ’ would presumably not include primary investment induced by innovations-let us say, building of automobile factories in the early stages of the automobile long wave, or ‘Kondratieff .’ But would the petroleum refineries, rubber plantations, and roadside restaurants brought into being by the automobile Kondratieff go into ‘ C ’ or into ‘k’? Harrod says ‘k’ will include ‘capital outlay which no one expects to see jus t sed or not justified in a fairly short period’ (p. 79). How long is that? As will appear below, it is not a matter of indifference how investment is distributed between ‘ C ’ and ‘k.’

There is another problem that arises in connection with ‘C : and ‘ C,’ The ‘relation’ usually expresses the extent to which investment increases as a consequence of increases in demand for the final products of plant and equipment of a given type. For the ‘relation’ to operate in the economy as a whole (without any change in the period of investment, which is not closely related to rates of consumption, and which Harrod excludes from this part of his analysis), there must be a change in the rate of consumer spending. The relation might be expressed as I = r.dC,. Hakod argues throughout as though ‘an increase in income necessarily entailed an increase in consumption, and also as though an increase in investment would always bring with it an increase in consumption. Why else would the increase in investment (C,) resulting from an escess of ‘G’ over ‘G,,’ (escess of ‘C,‘ over ‘C’) carry the system further from equilibrium?

Harrod’s point is, it will be remembered, that the greater investment brought about by C, > C will raise ‘G’ still further above ‘G-.’ In the contest of his argument, this proposition must mean that the increase in investment in the nest period will bring with it an increase in the rate of expansion of consumer spending

( *X’’). Now, if the increased investment is deficit-financed, it is C,

quite likely that the .increase in rate of expansion of consumption

[ 3 3 1 that accompanies an increase in investment

+dl be positive; for then the multiplier will operate on the increase in ‘I’ and so raise consumer spending substantially. But in most of Harrod’s ar-gument, savings and investment are always equal; if entrepreneurs consider their investment too low, they also consider their saving too low. An increase in investment financed by an equal and simultaneous increase in saving mill not raise income a t all, and consumption will actually fall. In this event, investment in period two will be too high, rather than still too’low, and will be reduced rather than raised in period three, and so on. The initial excess of G over G, would in this case set up a series of clamped ffuctuations,

184 THE ECONOMIC RECORD DEC. and in the absence of a new disturbance, the system would tend

towards a new equilibrium with the actual ~

equilibrium I - = ’, and so with G = G, and GC = G,C,. To take another example, i f half the new investment is fhanced

by new saving and the (instantaneous) multiplier is 2, national income will rise by exactly the amount of the increase in income and consumer spending ‘will remain unchanged; and so on. All kinds of models could be constructed, each giving a different result. Harrod’s analytical system is not self-contained. At many points in his argument, conclusions depend on unstated assumptions about entrepreneurial behaviour, and about the value of functional relationships not explicitly set forth.

Harrod seems to feel that he has excluded the possibility of new investment being financed by new savings, by arguing that -is small

relative to G. ‘Without any great revolution,’ he says, ‘ G might easily change from 2 to 6 per cent. This clearly could not cause saving to be trebled. The extreme case of saving being as low as 2 per cent of income, and all extra income, due to a rise in G, being saved may be ruled out. If saving is greater than 2 per cent, then f o r saving as a fraction of income to increase as much as G, consumption would have t o be cut as income rose, and this, too, may be ruled out’ (p. 79). The only case in which ‘s’ could vary proportionately with ‘G,’ he says (p. SS), is where ‘k’ is almost as great as ‘s’; that is, when the bulk of investment has little to do with current demand (hence the importance of the allocation of investment between ‘k’ and ‘ C ’ ) .

There are several dubious aspects of this argument. So long as growth depends on investment to meet current requirements, it seems to the reviewer that it would take something of a revolution to change ‘G’ from 2 per cent t o 6 per cent. Since investment not based on increasing demand for final products is ruled out of ‘(2,’ a trebling of ‘G’ really means a trebling of the rate of increase in consumer spending. Nothing we know about the consumption function implies that degree of instability in it, except perhaps when a cumulative inflation is already under way.

Secondly, Harrod’s a r m w e n t about the cumulative nature of a divergence of G, from G has nothing to do with the effect of a change in G on s ; to argue that a G > G , must raise investment, and so must raise G, because a rise in investment induced by the rise in G could not raise ‘s’ proportionately and so prevent the rise in G, is completely circular reasoning. The question is, must the investment induced by G > G,(C, > C) raise GI We have seen that the answer depends o,n the extent to which entrepreneurs finance

I = S equal to the P

Y

ds . d t


their investment by new saving and on the size of the multiplier; it also depends, incidentally, on the value of the relation coefficient itself, which was ignored in our illustration.

In the third place, there seems no a priori reason why in the real world the b d k of investment should not be independent of current requirements. Of course, Harrod is assuming ‘neutral’ inventions a t this stage; and he points out, quite rightly, that in this case a constant rate of technological progress would not require net savings, since replacement reserves would allow for obsolescence, But why should there not be an increasing rate of technological progress? Of course, if the stream of innovations is neutral, it absorbs no capital by definition. But a swelling stream of neutral inventions could absorb any amount of capital whatsoever, provided the stream swelled fast enough.

The manner in which new investment is financed is crucial to Harrod’s analysis. Unless he can demonstrate beyond a shadow of doubt that it is impossible for enough of an increase in investment

to be financed by new savings to make - (3) zero or negative,

he can argue that an initial divergence of G and G, may start a cumulative movement, but not that it must start a cumulative movement.

Harrod’s third fundamental equation is G,C, is equal, or is not equal, to s, in which ‘G,’ is the ‘natural rate of growth,’ or ‘that steady rate of advance determined by fundamental conditions’ (p. 87). Here again one wishes that the author’s terminology were less vague. What ‘ G,’. really seems to be is the rate of increase in output a t full employment, given the rate of population increase and the rate of technological progress. A hetter term would have been ‘potential rate of growth’; there is nothing very natural about full employment. It will be noted that whereas Harrod seems to feel that G,C, must equal GC, he stresses the possibility that G,C, may not equal GC, by making G,C, equal, or not equal, to s.

With the introduction of G,, Harrod is able to develop a theory of increasing under-employment. If G, exceeds G, (as it well may when population growth tapers off, or the rate of improvement in technique or discovery of new resources tapers off), G will also tend to lie below G,, C will be chronically above C,, and the economy will be chronically depressed. (After all, G can exceed G, only in the recovery phase of the cycle.) Conversely, in a rapidly espanding economy (where population growth, or technological progrc:s, or geographic expansion is at a high level) there will be a chronic excess of G, over G,, and also of G over G,, and thus a chronic excess of C, over C, and a perpetual tendency for inflationary boom to develop. We might call economies of the former type ‘deflationary

186 THE ECONOMIC RECORD DEC. gap’ economies (to avoid the term ‘excess savings,’ which is mis- leadings) and the latter type ‘inflationary gap’ economies.

Harrod contrives to get a skeletal theory of economic fluctuations, as well as a theory of trend, out of his analysis. In the recovery phase, G > G,. When full employment is reached, G = G,. If G, > G,, then at full employment G, > G, C, < C, and a slump is inevitable. Moreover, G, tends to rise in the later phases of recovery, because ‘companies are likely to save a large fraction of short period increases of net receipts’ (p. 89), and G, rises with ‘s.’ Thus it is quite likely that G , will rise above G, when high levels of employment are reached; and since at full employment G = G,, a slump ensues. If immobilities, frictions and ‘bottlenecks’ reduce G before i t equals G,, the downturn may come before full employment is reached. If G , is far above G,, G may never rise fa r above G,, and depression may begin ‘long before’ full employment is reached.

On similar reasoning, Harrod argues that ‘saving is a virtue and beneficial so long as G, is below G,’ (and therefore below G at full employment) because saving raises G, (p. 88). Why? Harrod does not bother to tell us. Of course, since G,C,= s, a n increase in ‘s’ must either raise G, or C,. By definition, it cannot raise C, unless G rises. In other words, an increase in saving does not cause a rise in G,, it is a rise in G,, by definition. Such analysis leaves the reviewer with a vague sense of discomfort. However, Harrod’s general conclusion about the ‘virtue of saving’ should surprise no one; i t is a ‘good thing’ in an ‘inflationary gap’ economy, and a ‘bad thing’ in a ‘deflationary gap’ economy.

The causal relation between G, and s is one of many problems that could have been made clearer by an elaboration of the central concept, ‘G,.’ The term ‘warranted rate of growth’ is not a very happy one for what Harrod seems t o have in mind. Nor is ‘ the line of entrepreneurial contentment’ a very clear-cut definition of ‘G,’ (p. 88). In his Economic Journal article, he defines G, as ‘that rate of growth which, if i t occurs, will leave all parties satisfied that they have produced neither more nor less than the right amount’; it is the rate that ‘will put them in the frame of mind which will cause them to give such orders as will maintain the same rate of growth.’ Thus ‘G,’ is subjective, but not, apparently, e x ante; it is the rate of growth that makes entrepreneurs satisfied with what has happened, rather than a plan for the future. Harrod also esplains in his article that he uses ‘the unprofessional. term warranted instead of eqni- Librium,’ because the equilibrium is ‘a highly unstable one.’ Stable or unstable, the term ‘equilibrium’ conveys more meaning than ‘ warranted,’ and future discussion would be clarified by a reversion to this term.

9. Cf. B. Hipgina, ‘To Save o r Not ta Save? C a d i a n Journal of Ecmomics and Political Science. February 1948.


While reference to the article makes Harrod’s concept of ‘G,’ a bit clearer, it still does not tell us what Harrod thinks are the determinants of G,; and what determines G, is obviously all-important; for ‘C,’ depends on ‘G,’-it is, indeed, d e h e d in terms of ‘ G m l ; Q and C cannot be changed except as a result of entrepreneurial decisions, and these decisions depend on G,. Thus what happens in Harrod’s dynamic economy depends ultimately on ‘ G,.’ Harrod nowhere presents an analysis of the determinants of ‘Gm’ but in the course of his discussion he does indicate the following relationships :

G, vanes (1) inversely with C, (2 ) directly with s, (3) inversely with the volume of public works, (4) inversely with the volume of investment that is

independent of the current rate of growth (k), (5) directly with the rate of interest (‘r’) (since ‘k’

and ‘Cr’ vary inversely with ‘r,’ and ‘s’ probably varies directly with ‘ r ’ ) .

The first of these relationships is arithmetic. Given s, G, must vary inversely with C, just as G varies inversely with C. There are no clues to entrepreneurial behaviour here. The second relationship has already been discussed; it, too, seems to be a matter of definition rather than of business behaviour. Relationships ‘3’ and ‘4’ really amount to the same thing. Public works are one kind of investment that need not depend solely on the current rate of growth of income, and may therefore be included in k. Since G,C, = s - k, by definition any increase in k must, other things being equal, be accom- panied by a reduction in G,. The fifth relationship is a product of several others :

(a ) ‘s’ varies directly with ‘r,’ and since G, varies directly with ‘s,’ G, varies directly with ‘r.’

(b) ‘k’ varies inversely with ‘r,’ G, varies inversely with ‘k,’ and ... G, varies directly with ‘r.’

(c) ‘Cr’ varies inversely with ‘r,’ G, varies inversely with C,, and ... G,varies directly with ‘T . ’

The relationship between s and,r is a true causal relationship; S ( r ) is a savings function with psychological meaning. The same is true of the k ( r ) function, which is really the marginal efficiency of capital schedule. The C,(r ) function is our old friend the period of investment, which also has meaningful content. But G,(r) has no

meaning of its own whatsoever j given the other relationships, the - is given by definition. Thus not one of these ‘Gm’ relationships is a truly causal one, with meaning in terms of entrepreneurial behaviour.

dGw dr

188 THE ECONOMIC RECORD DEC. Finally, Harrod adds two refinements. I f ‘d’ represents the

fraction of income needed for capita1 involved in lengthening the production process (‘deepening’) , then G,C ~ = s - d. If inventions are capital-saving, ‘d’ is negative, and the equilibrium rate of growth is enhanced. Thus any tendency towards chronic under-employment resulting from G, > 0. will be aggravated by capital-saving inventions. Harrod thinks falling interest rates might tend to lengthen the period of production and so keep ‘d’ positive. This is no place to reopen the Hayek:Knight-Kddor-Shackle controversy, but it is at least doubtful whether any feasible reduction of interest rates would have a significant effect on production techniques, especially if inventions themselves are capital saving.

In Chapter IV, on ‘The Foreign Balance,’ Harrod points out that when we move to an open economy, the appropriate equations are GC = s - b and G,C, = s - b, where ‘ b ’ is the foreign balance. The equation expresses what is already well known: in a country with chronic under-employment, (G, > G , ) , a favourable balance of trade on goods and services account helps t o reduce the deflationary gap.

IV Harrod has little new to offer by way of long-run policy to fill

a chronic deflationary gap. Wage-policy, he thinks, would not be an effective instrument for this purpose. To alter trends, once-over reductions are useless; a year-by-year reduction in wages would not affect G , directly (presumably i t might ultimately affect population growth or trends in labour productivity) and would be more likely to raise than to lower G,, by raising ‘the goods value of money’ (p. 9 3 ) . While the reviewer is a firm believer in rigorous separation of economic analysis from quest-ions of political expediency, ‘he cannot resist adding that very few governments indeed would dare or wish to attempt such a policy even if it would work.

Harrod is doubtful about the expediency of income redistribu- tion as a means of reducing the propensity to save. For one thing, if the number of rich people able t o save declines, corporate saving may increase. More important, in Harrod’s view, is ‘that there are deep laws relating the distribution of power (money is power) t o the stability of a political organism’ (p. 131). There remains the possibility of a declining interest rate; but ‘we must face the possibility that neither deepening nor saving mill react suf6ciently t o a falling interest rate’ (p. 144). We must also face the possibility, Harrod thinks, that the ‘euthanasia of the rentier’ would result in a deterioration of the quality of o u r civilization. The rentier class is an independent class, the class from which much of science and culture and most of our ‘modes of decent living’ have been derived. ‘We wish a general levelling up, not a levelling down. If . . . we


no longer have an established mode of life that is graceful and charming and delightful, then we take the salt out of socialist hopes’ (p. 150).

Yet reduction and ultimate abolition of interest is the only real solution for chronic under-employment that Harrod offers us. For if government debt contracted to sustain purchasing power is interest- free, then we need no longer be concerned about a cyclical balancing of the budget, and can fill the long-run deflationary gap by deficit- fkanced government spending. Thus Harrod leaves us with a dilemma; the policies needed to maintain a high level of income and employment in a mature economy may prevent us from enjoying t o the full the high level of civilization and culture that are the natural fruits of a mature society.

v What are we t o say about Harrod’s essay as a whole? It seems to the reviewer that there can be no doubt that Harrod

has written a very important book. Indeed, the only new book the reviewer has read in recent years with the same mixture of irritation and excitement, the same wavering between the feeling that there is nothing in the book that is both new and correct and the feeling that there is something in the novelty of approach that will prove enormously fruitful, was The General Theory itself. Like the General Theory, Harrod’s Dynamic Economics will need a good deal of elaboration and revision before the tools i t offers will be perfect enough for the journeyman economist to carry in his kit.

Of his fundamental equation, GC = s , Harrod says, ‘I should like to think that it might serve as a target for frequent attack, like Fisher’s famous truism, M V = PT.’ This is, in a way, a modest enough hope. Fisher’s equation of exchange proved rather sterile ; it isolated some important quantities for analysis, but told us nothing of the functional relationships among them or of the functional relationships determining their magnitudes. Some economists might even argue that until the significant causal relationships of Keynesian and neo-Keynesian economics were discovered, the Fisher equation did more harm than good, leading to over-emphasis of the quantity theory of money. It seems likely that Harrod’s hope will be ful- Bled, and that his fundamental equations will be attacked on much the same grounds. They, too, merely isolate some si,onificant quantities for analysis, but fail to set forth the fundamental functional relationships among them and the causal relations that determine their magnitude.

In particular, the equations do not in themselves isolate the fundamental fact that gives rise to secular problems: viz. that the rate of potential growth and the volume of saving both depend on

B

190 THE ECONOMIC REC0R.D DEC., 1948

the rate of technological progress, the rate of population growth, and the rate of discovery of new resources; while investment depends on the rate of change in these rates. It is fo r this reason that if the rate of expansion is increasing, there will be chronic over-investment and a chronic inflationary gap; and that if the rate of espansion is decreasing, there will be a chronic deflationary gap.10 Of course Harrod ’s argument demonstrates these same conclusions ; but his equations do not isolate the real source of the trouble.

I n one respect, the Harrod equations are inferior to the Fisher equation. The variables in the latter are clearly defined and easily measured ; Harrod’s quantities are considerably less clear and much more di5cult to measure. Indeed, the fundamental variable G,, and the accompanying C, are probably not measurable a t all. Against this deficiency, however, must be set the fact that Harrod’s equations reveal much more fundamental problems than Fisher’s, and are consequently very much more thought-provoking.

In his Preface, Mr. Harrod regrets the fact that he has ‘not been able to keep up &th the foreign literature on economic dynamics. The reviewer regrets it too. It would have been both interesting and helpful to hear from Mr. Harrod what he considers to be the fundamental differences between his approach and that of, say, Professor Hansen, or Dr. Kalecki, or Professor Domar. It is clear, fo r example, that in so fa r as it is concerned with mature economies-as it mostly is-Harrod’s theory is a compressed and formalized version of Hansen’s famous stagnation thesis, with the geographic frontier (new supplies of resources) left out. How useful it would have been if Mr. Harrod had expressed his views regarding the relation of his analysis t o the controversy over the Hansen stagnation thesis !I1

But it is senseless to cavil a t pressures on BIr. Harrod’s time that he undoubtedly resents far more than any reader of his book possibly could. Let us hope that the course of world events will not once again deflect Mr. Harrod from his main intellectual interests, and that he will find time to write himself some of those between-the- lines paragraphs in his latest book. Meanwhile, we can but be grateful to Mr. Harrod for providing us with the onerous but greatly rewarding task of studying Towards a Dynamic Economics.

BENJAMIN HIGGTNS. Melbourne University.

10. The reviewer h o w to present a simple set of equations in which these relationships are set forth sxplicitly in a later article.

11. The omission of the rate of discovery of new resources u a determinant of potential and actual output is more serious than Harrod seems to realize. Development of new resources h a provided one of the major outlets for profitable investment in the past: and it is only by abstracting from the rate of discovery of new resoruca that Harmd can legitimqtely exclude diminishing returns from land ad a significant element of dynamic economics. So long M the supply of natural resources is expanded as fast as capital accumulates, no reductions in the marginal prodUctiVitY of capital d I Occur on this score: hut as awn as the supply of natural rmourcm fails to keeD pace with capital accumulation. then-dher thinga heing equaI4iminishing returns to additional investment m u t set iq.

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TOWARDS A DYNAMIC ECONOMICS