Paths of accumulation and growth: Towards a Keynesian long-period theory of output

Abstract

According to the principle of effective demand, the equilibrium level of aggregate output is a multiple of the expected autonomous demand for the period under consideration. Aggregate demand matches aggregate supply in equilibrium, but the equilibrium may and usually does lie below the output corresponding to full capacity and full employment. However, in the long term firms are presumed to use capacity at the normal or desired degree. Can the principle of effective demand be extrapolated to conclude that the rate of growth of output will depend on the expected rate of growth of autonomous demand? A positive answer would be a significant step towards a Keynesian long-period theory of output. This paper attempts to make an advance in that direction. Starting from a ‘prospective accelerator’ that incorporates expected increases in autonomous demand and takes account of an excess of capacity in order to eliminate it, this paper shows that the path of autonomous demand determines both the actual and the warranted rates of growth.

Acknowledgments

This paper has a long history. It draws on De-Juan (1999), which in turn draws on the author's 1989 doctoral dissertation. Edward Nell, to whom I am especially indebted, supervised the thesis. I am also grateful to two anonymous referees for advice on matters of emphasis.

Notes

¹On the contrary, full employment cannot be considered a condition for efficiency and profit maximization at the firm level. Nor is it a hard constraint for economies that are growing at a moderate rate. By paying a small premium over the going wage, entrepreneurs can attract additional hours of labour from already employed workers and can draw immigrants and new participants into the workforce. This paper will abstract from such issues and from natural resource constraints in order to focus on capacity constraints.

²For example, in one of the most widely used macroeconomics textbooks, Gregory Mankiw (2003) summarized the field's main lessons as follows: ‘Lesson 1: In the long run, a country's capacity to produce goods and services determines the standard of living of its citizens. Lesson 2: In the short run, aggregate demand influences the amount of goods and services that a country produces’ (p. xxiii).

³Garegnani's suggestion has been pursued in Eatwell & Milgate (1983) (see in particular the editors' Introduction and Conclusions) and in the journal Political Economy (see Vianello, 1985; Amadeo, 1986; Ciccone, 1986; Committeri, 1986; Kurz, 1986). A second set of discussions on the topic began a decade later in Contributions to Political Economy (see Serrano, 1995; Trezzini, 1995, 1998; Barbosa-Filho, 2000; Park, 2000). All of these interventions will be commented upon below.

⁴Amazingly enough, the investment function of the static IS-LM model disappears in neoclassical growth models.

⁵This paper abstracts from technical change, as is usual in the literature on normal prices and normal output. This decision can be justified by assuming either that (1) in the period being considered the effects of technical change are negligible or (2) technical change is Harrod neutral. The latter assumption implies that, despite the variety of changes occurring at the firm level, in the aggregate a constant desired capital:output ratio k is observed (as will be seen, k is the only technological variable that appears in the accelerator). Note that Harrod neutrality conforms to the stylized facts that Kaldor (1961) observed for the post-war period and can be extended to the second half of the twentieth century. In most advanced countries, technical change has been embodied in new machines that have raised the productivity of labour. The productivity gains have accrued principally to workers, who have consumed most of the wage increases. Both capital and output have grown significantly and proportionally, so that their ratio k has remained fairly constant. The same has happened to the shares of profits and wages in income.

⁶This paper defines u _t =Y _t /Y*. Y _t is the current level of income stemming from the existing stock of capital used at any rate k _t : Y _t =K _t /k _t . Y* is ‘capacity income’ stemming from the normal use k of the capital stock: Y*=K _t /k. These definitions allow us to write u _t =k/k _t .

⁷To simplify the exposition, this paper will comment mostly on the cases where there are undesired inventories and excess capacity. The reader will have no problem reversing the exposition whenever inventories are below normal and capacity is being overutilized.

⁸ , where K _t =k _t Y _t is the actual stock of capital at t and is the desired one. Dividing by Y _t obtains . Therefore

⁹A comparison with the usual formulation of investment in the neo-classical synthesis may be helpful. In the IS-LM model total investment is expressed as TI _t =I _o–bi _t , where I _o is the autonomous investment (a datum) and i _t is the actual interest rate. In the model here total investment is made up of modernization investment (or ‘autonomous investment proper’) Z _t and induced investment. This is the I _t captured by the accelerator that can be made flexible in order to take into account possible deviations of current interest rates from the conventional level (i*). The following expression looks more suitable: TI _t =Z _t +k _t g _[zcirc] Y _t −b[(i−i*)/i*]).

¹⁰In order to render the model closer to reality the paper could follow Kalecki (1971) and disaggregate the propensity to consume, which is a weighted average of the propensities to consume out of wages (c _w ) and out of profits (c _p ): c=c _w (W/Y)+c _p (P/Y), where W is wages and P is profits.

¹¹Substituting in the investment function (K _t /k _t ) for Y _t , we can write Y _t =cY _t +k _t g _z (K _t /k _t )+Z _t =cY _t +g _z K _t +Z _t =(1/[1–c])(g _z K _t +Z _t ).

¹² Equation (3) should not be applied in a mechanical way. In this case it would be better to consider equation 2: I _t =k(D _t+1–Y _t )–E _k,t . If the excess capacity E _k,t is high enough, I _t will approach zero.

¹³Alexander (1949) made a similar claim. Harrod (1973, pp. 19–20) recognized that the objection was sensible enough. Unfortunately, growth economists continued emphasizing the centrifugal forces associated with the knife-edge parable.

¹⁴The term ‘prospective accelerator’ has been chosen to emphasize that, in their investment decisions, firms are forward looking. They decide on investment on the basis of the expected increase in aggregate demand, which is a multiple of autonomous demand I _t =kΔD=kg _z Z _t μ*. Then they discount undesired inventories E _i,t–1 and excess capacity E _k,t , so the preceding expression becomes I _t =[D _t+1−(D _t −E _i,t−1)]−E _k,t . Autonomous demand, however, continues growing at the rate g _z and firms must make up for the goods not produced in t. This explains why in equation (3) undesired inventories (ϵ>0) and excess capacity (u<1 or k _t >k) push up investment.

¹⁵Trezzini (1995, 1998) dismissed the Hicksian supermultiplier because it does not grant autonomous demand the possibility for growing at any rate. Note that we are not preventing a single innovative firm from growing as fast as 50, 100 or 200%. The limit applies to the group of innovative firms, the production of which accounts for a non-negligible share of current output. We could even permit the whole group to grow for a time above the limit set in equation (7) by reducing k _t . However, the flexibility of technology has a limit. Labour force and natural resources constraints will also make themselves felt after a point.

¹⁶ Table 3 in the Appendix examines the case where aggregate demand consists solely of induced consumption and induced demand. Since there is no autonomous demand proper, the adjustment cannot be made via z. It will occur through inventories and capacity. Notice, however, that this does not impair the stability of the system. The share in income of undesired inventories and excess capacity are maintained in reasonable limits.

¹⁷Trezzini (1995) arrived at equations similar to this paper's equation (9) and (10), though he found a paradox that calls the validity of the model into question: ‘A paradox implicit in Hicks's model now also becomes clear: while it is stated that the autonomous demand expansion is the leading factor in economic growth, it is simultaneously stated that the rate of growth is maximum when the components determining economic growth, and therefore their rate of growth, are zero. The origin of this paradox lies exactly in the assumption of normal capacity utilization’ (p. 48). Our position is that, within the broad limits analysed in the previous section, g _z can take any value: z _t will adjust to make possible the new path of growth of autonomous demand in normal conditions. ‘Normal capacity’ is not assumed to obtain over the course of the traverse. On the contrary, changes in capacity use are the first mechanism of adjustment.