Profit rate dynamics in US manufacturing

ABSTRACT

The attributes and dynamics of the profit rate distribution provide indispensable information on how the economy works. Edith Penrose, in The theory of the growth of the firm¸ took agency, managerial capabilities, heterogeneity and open-endedness as characteristic of the economy. Schumpeter had a similar view. Neoclassical theory, in contrast, envisages convergence to a standard rate of return, invoking inter-industry capital flows and diminishing returns as the main mechanism. I analysed the data on US manufacturing, 1987–2015. There was evidence of convergence, attributable to loss of supra-normal profits in two industries. The features of the distribution confirm Penrose’s view. Neoclassical theory fares poorly: the data do not support ‘a standard rate of return’, and no plausible macro shock exists that could have produced the observed dispersion. The symmetry of the observed distribution indicates that neither market power nor intangible assets play major roles in determining the shape of the profit rate distribution; risk, however, is relevant if reformulated. Intersectoral capital flows were weak, and there was no evidence of diminishing returns. Penrose’s conception of heterogeneous managerial capacity refers to a concept of economic power distinct from market power, corresponding to differential ex ante strength; differential profit outcomes represent ex post strength.

KEYWORDS:

• Penrose
• rate of return on capital
• profit rate
• convergence
• capital flows
• diminishing returns
• market power
• intangible assets
• managerial capacity
• entrepreneurial profit
• economic power

JEL CLASSIFICATION:

• D22
• L10

1. Introduction

There is no more important proposition in economic theory than that, under competition, the rate of return on investment tends towards equality in all industries. Stigler (1963, 54).

1.1. The research problem

Profitability is one of the most important attributes of a firm, and is a major criterion of its success. The behaviour of the rate of return on investment, or more succinctly the profit rate, is highly informative about economic performance in the aggregate: it can provide evidence about how the economy works. There is, however, little high-quality empirical research on this topic. In particular, the available evidence (such as it is) does not support Stigler’s classic assertion. I set out to test Stigler’s neoclassical view and its major rivals, the firm-centred approach of Edith Penrose (1959) and Schumpeter’s views on creative destruction (1934, 1943), using a large dataset, nationally representative of US manufacturing, over a period of almost 30 years.

Penrose’s contribution is important, because it developed from close and systematic analysis of actual firms. The theory of the growth of the firm was a distillation of multiple observations, formed into a causal account of the processes involved when firms expand. In parallel, the business historian Alfred Chandler came to similar conclusions from a detailed examination of the rise of large corporations in the US, as well as comparative studies with the UK and Germany. In addition to strong empirical foundations and a central focus on the firm, their perspectives share the feature that they are fundamentally concerned with change. This dynamic focus is also an attribute of Schumpeter’s theory of entrepreneurial profit.

The paper is structured as follows. After some initial methodological observations, I outline the patterns that would be predicted from the dynamic theories of Penrose and Schumpeter. The predictions of neoclassical theory are then presented, together with the main assumptions that, if violated, could lead to deviations from the standard neoclassical model. I then analyse data on US manufacturing at the industry level for 1987–2015: after describing the dataset, I present the observed distribution and its descriptive statistics, plus evidence of a convergent trend. I then examine the differential flow of new capital across sectors. Finally, I analyse the relationship of the profit rate to the capital stock, to test the hypothesis of diminishing returns. I end by discussing the implications of the empirical findings for the various theories.

1.2. Preliminary observations on methodology

Firms assess the potential and the opportunity cost of investments according to their likely profitability, ex ante, often using such measures as the Internal Rate of Return (IRR) or the increase in Net Present Value (NPV). But it is difficult to obtain data that accurately reflect the ex-ante calculations of firms, and economists who have adopted this perspective have had to operationalise it in terms of actual expenditure (e.g. Fisher 1969, 35).

An alternative concept is to examine the achieved rate of return on capital, ex post, using available accounting data on the operating surplus (total revenue minus total costs) and on the cost of investments. Although this may not be identical to firms’ ex-ante calculations with complete accuracy, the empirical difference is small (Fritsche and Dugan 1997). And an advantage of the ex post approach is that modern financial reporting, based on the principles of accrual accounting, corresponds closely with managers’ concept of the profit rate (Bryer 1993).

In addition, the use of ex post accounting data has the advantage that it reflects the outcome of actual economic events, to the extent that the limitations of data quality allow. For example, it allows account to be taken of macro shocks such as the dot-com boom and crash, China’s accession to the WTO and the financial crisis, the effects of which are unknowable to firms ex ante. In contrast, therefore, to the neoclassical view that regards firms’ ex ante, subjective calculations as the gold standard, the use of accounting data is ‘entirely justified, not as a mere feasible expedient, but as the required method of measuring capitalists’ rate of return’ (Wells 2007, 22).

Such an analysis can be at the industry or firm level. Each has its advantages and its limitations, so that a comprehensive analysis of the issue needs to include both.

The analysis presented here is at industry level. This is the more appropriate for an initial analysis because a representative sample is obtainable, which is of vital importance when presenting and analysing descriptive statistics. It capitalises on the resource provided by the Bureau of Economic Analysis, that has comprehensive coverage going back as far as the 1980s, with categories that are uniform for the whole period. It has the limitation that only a two-digit industry classification is available, but this is outweighed by the advantages of the BEA dataset for a preliminary study.

The findings at the industry level do not necessarily apply to the firm level, and those at the two-digit level may not be the same as, for example, those at the four-digit level. In particular, a finer classification would tend to generate a distribution with greater dispersion, and one would expect to find less dispersion at the industry level than the firm level because of the within-industry heterogeneity of firms. To that extent, the present analysis has a conservative bias towards underestimating the heterogeneity of profit rates.

However, that would not affect this paper’s assessment of neoclassical theory, which would predict a narrow distribution clustered near the standard rate of return at either level, because it states that the tendency towards convergence should be pervasive across the whole economy. A further possible issue is that the reclassification of a single large firm could temporarily distort the observed profit rates of the industries involved (Stigler 1963).

A limitation of firm-level analysis is that firm-level datasets tend to be systematically incomplete: smaller firms’ inclusion depends on stock-exchange listing and/or minimum turnover, profit or number of employees. Smaller firms are thus likely to be underrepresented, so that the sample is inevitably biased, implying that a representative sample is unobtainable. There are also specific problems associated with very small firms, because they not only have a relatively wide dispersion, but also many extreme and implausible values (Wells 2007, 81; Greenblatt 2013); and they include sole proprietorships, for which profit and managerial income are hard to distinguish. In addition, firm-level analyses face the problem of firms’ entry and exit, so that it is difficult to assemble a cohesive data series on the profits for each firm; in some cases, survivor bias can also be a serious issue (Cubbin and Geroski 1987).

Some of the causal forces operate at firm level, and in these cases an industry-level analysis is an aggregation of the influence of the actions and fortunes of many firms, which would attenuate the results. A corollary is that it is more difficult to obtain robust findings. Conversely, other causes operate at the industry level, for example a sector that is declining would be expected to lose investment to a more promising up-and-coming one.

The availability of data over this long time period, nationally representative of US manufacturing, is a key advantage of these analyses. It is possible to assess long-term trends in the profit rate and in its dispersion, the trajectories of each industry, patterns of capital flow between industries and the magnitude of diminishing returns, as well as to evaluate the effects of macro shocks. The paper therefore provides important evidence concerning this hitherto-neglected research area.

2. Predictions from theory

2.1. Dynamic theories

2.1.1. Penrose: ‘The theory of the growth of the firm’

Penrose’s (1959) theory provides a causal account of the process of expansion, for firms that are growing; it does not seek to explain which firms are likely to grow. Profitability plays a role, in that managers are assumed to be primarily motivated by the pursuit of total long-term profit – they deploy the resources available to them, including their own capabilities, to undertake profitable investments that expand the firm itself as well as its profitability. However, Penrose does not focus on the rate of profit, or the comparative profitability (the distribution) of different firms or industries. Nevertheless, the key features of her analysis allow a qualitative prediction to be made.

The attributes of Penrose’s theory that are relevant to the profit rate distribution and its dynamics are agency, managerial capabilities, heterogeneity and open-endedness. Agency is central: managers take initiatives in the light of the resources available to them plus their assessments of potentially profitable opportunities. This is neither optimising – and therefore automatic – behaviour, nor a stimulus-response conception. The quality of initiatives depends on managerial capabilities, the degree of ability to make their projects successful, including fund-raising ingenuity (Penrose 1959, 34).

Heterogeneity is emphasised throughout her work: each firm is unique, its strengths depending on its specific resources, which in turn depend in a path-dependent manner on previous actions (e.g. pp. 173–4). In addition, cumulative growth occurs because success breeds further success, amplifying between-firm inequalities. Her theory is open-ended, because the future is uncertain; the quality of each ex ante initiative influences but does not determine the ex post consequences, including the degree of profitability.

One would therefore expect a wide distribution of profit rates, both between firms in a given industry, and between industries. There is no inbuilt tendency for this to change over time, except that highly dynamic economies, bristling with multiple initiatives, might be expected to have especially divergent profit rates. Importantly, differential firm size and profitability are not necessarily indications of monopoly power, but rather of ‘more able and enterprising managers and entrepreneurs’ (p. 164): they result from the unequal ex ante strength of different firms’ resources and how they are used, together with the operation of chance. An implication is that a hierarchy of profit rates is not necessarily attributable to market power; a second source of power is superior managerial capabilities. They are not mutually exclusive, because firms that have grown as a result of superior management may then use their position to exercise market power in the conventional sense.¹

2.1.2. Schumpeter’s theory of entrepreneurial profit

According to Schumpeter’s The theory of economic development, first published in German in 1911, ‘Entrepreneurial profit is a surplus over costs’, these costs being taken to include rent of the land needed for production, risk, and ‘an appropriate wage for labour performed by the entrepreneur’ (Schumpeter 1934, 128). Schumpeter contrasts this with circular flow, a static condition in which ‘the total receipts of a business – abstracting from monopoly – are just big enough to cover outlays’; ‘since the new combinations which are carried out if there is “development” are necessarily more advantageous than the old, total receipts must in this case be greater than total costs’ (Schumpeter 1934, 129).

In terms of the implied profit rate distribution, Schumpeter is here proposing a dualistic structure: the static part of the economy that has zero economic rent, in other words equal to the standard rate of return, and the industries that have some degree of supra-normal profit. The implied distribution is therefore semi-continuous, with a spike at the standard rate of return plus a positive distribution. Statistically, this would register as positive skewness rather than symmetric dispersion.

Schumpeter’s views on the source of capitalist dynamism changed over time, and he came to see ‘the large-scale establishment or unit of control … [as] the most powerful engine of … progress and in particular of the long-run expansion of total output’ (Schumpeter 1943, 106). In this ‘Mark II’ version of his theory, he emphasised ‘competition which commands a decisive cost or quality advantage and which strikes not at the margins of the profits and the outputs of existing firms but at their very foundations and their very lives’ (Schumpeter 1943, 84). Although less explicit about profitability than in the earlier ‘Mark I’ account, his view remained that creative destruction involved innovation by new firms or industries that were more successful and thus more profitable than the incumbents they replaced. The prediction would therefore again be a positively skewed semi-continuous distribution.

According to Schumpeter’s theory, it is not essential that the identity of the industries characterised as ‘more advantageous’ remain the same. They could vary over time, with specific industries having a static circular-flow nature with zero entrepreneurial profit at certain times, and a positive profit at others. The existence of a group of more dynamic industries at each moment could be regarded as providing a divergent force in the profit rate distribution that counterbalances the prevailing tendency towards convergence.

2.2. Neoclassical theory

2.2.1. The standard account

Neoclassical theory states that under competition, profit rates across industries, and across firms within each industry, tend to converge to a single rate at any given time. There are two possible mechanisms.

The first is that any existing super-normal profit rates, due to market power (see next section), are eroded by new entrants. The situation thereby comes into closer alignment with the assumption of perfect competition. The profit rate distribution becomes more symmetrical as skewness decreases. It is contingent on the arrival of new entrants; were concentration to increase, the opposite tendency would be observed.

The second mechanism is that those with the higher rates of return should attract capital, and those with lower rates fail to attract it. This could be because capital is withdrawn from less profitable sectors and invested in more profitable ones, and/or because over a long period the amount of capital flowing towards failing industries dries up, while thriving sectors attract the available finance. This process ensures the allocation of capital to its most efficient uses across the economy. Diminishing returns then ensures that the copious inflow to dynamic industries brings their profit rate down towards the average for the whole economy and vice versa for struggling industries. Unlike the first mechanism, therefore, the change is not contingent.

Neoclassical theory thus predicts that the economy moves towards an equilibrium with zero dispersion, and zero economic profit (equal to a uniform ‘standard’ rate of return). At any given moment, however, this may not be observed, because shocks may have caused rates to diverge. These may be economy-wide macro shocks which differentially affect different sectors, such as a financial crisis or a pandemic. In the 2007–09 crisis, for example, the car industry became less profitable, but the food industry prospered (see below).

Alternatively, shocks may be at industry or firm level: innovations that affect profitability, for example via a change in costs or the introduction of a superior product, would be seen as shocks by neoclassical theory. The overall picture is thus of an economy with an endogenous convergent tendency towards a uniform equilibrium profit rate, that is also subject to exogenous shocks that generate divergence away from it.

The tendency towards diminishing returns – which is central to the second mechanism – is generally regarded as axiomatic, and has been assumed in such classic contributions as the standard neoclassical theory of growth (Solow 1956), and modern endogenous growth theory models (Romer 1986; Aghion and Howitt 1998), in which spillovers are just sufficient to overcome diminishing returns. It is also the basis for the Lucas ‘puzzle’ (Lucas 1990).

2.2.2. Deviations from standard neoclassical theory when its assumptions do not hold

Neoclassical economists allow for the observed behaviour of an economy to deviate from this theoretical account, if its assumptions are not met in practice. These include a perfectly competitive market and the ability of capital to flow freely from a less profitable to a more profitable use, equal risk, identical technology and uniform ability to make it profitable. The assessment of such behaviour may also be distorted by systematic errors in the measurement of capital expenditure and/or of its profitability.

2.2.2.1. Market power

In standard neoclassical theory, all firms in a perfectly competitive market earn zero economic profits. All firms are price takers, and there is free entry and exit, etc.

In practice, however, firms may well have some degree of market power, and therefore economic profit rates above zero. This could be due to barriers to entry and exit, collusion, economies of scale, sunk costs, etc. Market power would lead to a higher rate of return than obtains under perfect competition which corresponds to zero market power. There is no equivalent force acting in the opposite direction, i.e. negative market power leading to a less-than-standard profit rate, so that the distribution of rates of return would have the standard rate of return as its lower bound, and would be positively skewed.

2.2.2.2. Risk

In business as well as in finance, the degree of risk varies: the prospect of getting a return on one’s investment is less certain in some sectors than others. In finance, a frequent definition of risk is the probability that an actual return on an investment will be lower than the expected return, possibly due to interest rate risk, exchange rate risk, liquidity risk, etc. A higher expected profit rate would thus be needed to induce the investment. This would imply a baseline of zero risk, plus a variable positive degree of risk, suggesting a profit rate distribution with the standard rate as lower bound, and likely positive skewness. However, other ways of thinking about risk are more symmetric, that may be more realistic (see below).

2.2.2.3. Neglect of intangible assets

Estimation of the rate of return on capital necessarily depends on the accurate measurement of the capital outlay. In principle, this could be either under- or over-estimated. In practice, the literature is silent on overestimation and focuses entirely on underestimation, specifically on the grounds that firms’ expenditure includes items that contribute to future output and/or sales, but which are conventionally listed under current rather than capital spending. Such items are collectively grouped under the heading of intangible assets (Haskel and Westlake 2017), and they include advertising, R&D (Megna and Mueller 1991; Görzig and Gornig 2013), and organisational capital (Görzig and Gornig 2013), as well as software and intellectual property. Neglect of any or all of these understates the true capital expenditure, so the implication is that the observed rate of return is higher than the actual one, that is, positively skewed.

A classic study was carried out by Megna and Mueller (1991): they investigated the neglect of R&D and advertising in the US (1967–1988), focusing on pharmaceuticals, distilled beverages, cosmetics and toys at the firm level. Inclusion of advertising and R&D spend in capital did not eliminate the wide dispersion in profit rates. More recently, Görzig and Gornig (2013) have found that the observed (unadjusted) rate of return was reduced by about 20% in Germany 1999–2003, once they allowed for own-account production of ICT, R&D and organisational capital – in other words, after a proportion of specialised labour was reclassified as capital spending.

2.2.2.4. Heterogeneity in managerial capacity or talent

This is central to Penrose and Schumpeter, but in neoclassical theory identical technology across firms is often assumed. This is taken to imply a common cost structure as well as an exogenously given price, so that the rate of return is uniform. In practice, however, substantial between-firm heterogeneity is observed in growth rates, productivity, productivity growth, efficiency, market performance and the degree of innovativeness, (e.g. Davis, Haltiwanger, and Schuh 1996; Bartelsman and Doms 2000; Foster, Haltiwanger, and Syverson 2008; Dosi et al. 2012; Dosi, Grazzi, and Moschella 2015; Decker et al. 2016; Foster et al. 2017). This literature has not focused on the profit rate, but elsewhere there is some limited evidence on the firm-level profit rate distribution (Wells 2007).

Heterogeneity is present even with the same input prices, and irrespective of the level of industry disaggregation (Dosi, Grazzi, and Moschella 2015). The evidence also supports considerable heterogeneity in participation in export markets (Bernard et al. 2012; Melitz and Trefler 2012). This is clearly in line with the analysis of Penrose’s (1959), centred on variations in managerial capacity between firms, which also has considerable empirical support (e.g. Bloom, Sadun, and Van Reenen 2012).

It is less certain whether the same explanation applies to profit rate heterogeneity between industries. This would occur if there were a systematic tendency for some branches of manufacturing to attract and retain more competent entrepreneurs and managers. There is some evidence to suggest that this may be so, at least to some extent; for example, export propensity is associated with managerial competence (Driver and Temple 2013).

2.2.2.5. Inter-industry differences in monetary or non-monetary rewards

Another possibility is that compensating differentials affect the observed profit rate, either because the work is so unpleasant or hazardous that an additional monetary reward is required, or conversely that the experience of the work is sufficiently pleasant that lower remuneration is needed to attract people into that line of business (Stigler 1963). However, this is probably not relevant in the present context. In manufacturing at least, the profit primarily accrues to firms (employers), whereas it is the workers who would experience any unpleasantness or health risk, or conversely pleasure. Owners of coalmines are unlikely to develop silicosis or to be injured in underground accidents, and it also appears unlikely that the owners or managers of manufacturing firms vary greatly in the degree of pleasure they get from the particular branch of manufacturing that they happen to be in. Furthermore, even if such differences do exist, they are unlikely to vary significantly over time. It is therefore not considered further in this paper.

3. Empirical literature

The analyses presented in this paper primarily relate to two literatures. There are empirical studies of profit rate convergence, and there is a limited empirical literature on diminishing returns to financial capital.

3.1. Convergence

There is a large mainstream literature, primarily within macroeconomics, that investigates the extent to which capital is allocated efficiently across the economy, and the economic impact of misallocation (e.g. Hsieh and Klenow 2009; Eisfeldt and Shi 2018). The starting point is the notion that this capital reallocation is fundamental to the functioning of the economy, because it allows a shift from low to high productivity firms. It is therefore traditionally held to play a major role in growth of productivity and GDP (Stigler 1963). However, leading researchers in this tradition have recently shown that this role is empirically small – what they call ‘the reallocation myth’ (Hsieh and Klenow 2018).

In line with this re-evaluation of the role of capital reallocation, it is relevant to investigate the prior question, whether such reallocation occurs at all. Clearly, if it does not, then its proposed impact on productivity and GDP would not even arise. This would likely require paying attention to changes in production, as Penrose did, rather than to mere reorganisation of existing production – the reallocation notion treats the origin of high-productivity firms as being an external cause, rather than a central element in the growth of firms and economies. At issue here is whether economic dynamism results primarily from the actions of those whose decisions set the direction of the firm, or of those who have the money to pay for new investment when this cannot be financed by retained profits; and whether growth results from innovation in production or from flexibility bringing about a perfect market.

The capital reallocation perspective has hitherto dominated this literature, to the detriment of focusing on innovation in production. It is preferable to empirically investigate the basic features of the economy, making no assumptions about causal processes that may or may not be operating until they have been backed up by evidence. This direct methodology (such as a ‘data-first’ approach (Juselius 2011)), that imposes little model structure until it can be empirically justified, could be considered an instance of what has been called ‘evidence-based economics’ (Joffe 2014; Joffe 2017). In the present context, it involves directly investigating the profit rate at industry level, with a view to assessing what causal processes are compatible with the data.

In the previous empirical literature, much of the historical evidence is at the firm level and applies to the US. In many cases, the samples then available for research constituted a relatively small and probably unrepresentative sample of the economy. In addition, as will be seen, many contributions assume one dominant feature underlying their data, such as concentration, and structure their analysis around that, rather than starting with an open-minded examination of the rates of return.

The earliest analysis of US profit rates was at the industry level, and covered the period 1938–1956 (Stigler 1963, 57–58). Greater dispersion was observed for 1947–56 than for 1938–47, indicating the occurrence of divergence rather than convergence, with a coefficient of variation of 21.9% and 31.5% in the earlier and later periods, respectively; this analysis was restricted to ‘unconcentrated’ industries, but did not take account of barriers to entry. Stigler’s interpretation was that the smaller dispersion in the earlier period could have been due to ‘extremely heavy corporate excess-profits taxation’, but there is no evidence for this view.

Qualls (1974) investigated the persistence of the gradient of rates across concentration classes, rather than the distribution of rates of return as such, for 1950–65. The aim was specifically to investigate the effect of market power and how it may change. He found that the concentration-related dispersion of the profit rate persisted.

Mueller (1977) found a considerable degree of movement in the ranking of firms’ profit rates, using a firm-based sample for 1949–1972. Contrary to expectations, firms that started at the top or the bottom of the rankings were less likely to change position than those in the centre of the distribution. Risk was considered not to explain the persistence of relatively high profit rates. It is unclear whether there was overall convergence or divergence.

A similar analysis was carried out by Connolly and Schwartz (1985) for 1963–1982. They confirmed the finding of persistence of the high rates, but indicated that firms with low profit rates tended to converge towards the average rate.

In a later analysis comparing 1964 and 1980 (Mueller 1990), the degree of persistence of abnormal profit rates was observed to be much lower, although some persisting advantage in the top group (out of six) remained. Convergence had therefore occurred between these two periods. This contrast remained essentially unaltered when the comparison was confined to the 397 firms that were present in both samples, indicating that it was an actual change rather than an artefact of sample selection.

Similarly, convergence was observed at the industry level for 197 industries between 1963, 1967 and 1972 (Levy 1987). The speed of convergence was quite fast when separate industry intercepts were included, but slow in their absence. Jacobsen (1988) also found convergence at the firm level, albeit relatively slow, in 1970–1983.

Thus, the empirical literature suggests a mixed picture, with profit rates moving sometimes in the theoretically expected direction, sometimes in the opposite direction, and at other times appearing not to move at all. Overall, the differences in the findings could be due to the different methods used, or to differences in the details of the particular samples in each study – especially the firm-based analyses, in which the included firms might not be representative of the economy.

Alternatively, the differences may be real. There is a suggestion, albeit tentative given the methodological issues, that in the US there was divergence of profit rates between 1938–47 and 1947–56, relatively little change in the late 1950s and early 1960s, and then convergence starting sometime in the 1960s and continuing into the later period covered by the analyses presented in this paper.

3.2. Diminishing returns

The law of diminishing returns has a venerable history, dating back to Turgot in the eighteenth century and to Ricardo and others in the early nineteenth century (Brue 1993). It has been applied to two very different situations: in production where it has a physical meaning, and in the context of financial capital.

The classical descriptions focused on production, and relied on implicit physical properties. They were initially applied to the fertility of land. With a fixed quantity of land, the addition of increasing quantities of inputs, for example of labour and/or capital, was not followed by a proportionate increase in the yield. Many of these pioneering contributions were defined imprecisely and inconsistently, and ‘often confused average and marginal returns, homogeneous and heterogeneous inputs, short-run and long-run returns, and more’ (Brue 1993). In 1888, John Bates Clark extended this argument beyond agriculture, introducing the now-familiar concept of capital as a fixed factor of production, with labour as the sole variable factor. Subsequently, the concept of diminishing returns in the context of physical production has become accepted as an axiom, even if the theoretical proofs of it have sometimes been unsatisfactory, and the empirical evidence for it is mixed, even in agriculture (Brue 1993).

In the present context, diminishing returns no longer has its roots in a physical relationship, as with the addition of more labour or more fertiliser to an existing plot of land. Rather, the concept of capital here is essentially financial: that the availability of a greater quantity of capital leads to a decrease in its rate of return. Its validity generally tends to be assumed but not tested empirically.

The closest empirical literature I can find to this is in the international context: that the quantity of capital available in a country is inversely related to the profit rate. Most of the literature assumes this to be true. However, Nell and Thirlwall (2017; 2018) have directly estimated the productivity of investment for 84 rich and poor countries over the period 1980–2011, as the ratio of long-run GDP growth to a country’s gross investment ratio. They found no significant evidence of diminishing returns.

The assumption that diminishing returns applies in this context is deeply rooted in the mainstream literature. For example, it plays a central role in the canonical Solow neoclassical growth model (as well as new growth theory and the Lucas puzzle, as previously noted), and underlies its prediction that relatively poor countries with low capital endowments are destined to grow faster than rich countries with abundant capital, other things being equal. An implication is that whatever the original level of capital in an economy, it will tend to revert to the equilibrium levels of output and capital indicated by the economy’s underlying features. The repeated finding in cross-country growth regressions of a negative coefficient on initial income levels is often taken as conditional convergence, and therefore a confirmation of the Solow model. However, it is equally likely to result from a catch-up effect, for example from the adoption of technology from abroad (Benhabib and Spiegel 1994). The work of Nell and Thirlwall suggests that the latter interpretation may be the correct one.

4. Data

Data were obtained from the Bureau of Economic Analysis (BEA n.d.). Gross operating surplus (GOS) was derived from the table of the components of value added by industry, for 1987–2015. These data do not take account of depreciation, tax, etc. Table 3.3ESI provided the net stock of private fixed assets by industry for 1986–2014, at historical cost. These are year-end estimates of the running total of investments, net of depreciation. Table 3.7ESI provided data on investment in private fixed assets by industry for 1985–2016. These data are classified in 62 sectors; the 19 manufacturing sectors are the focus of the present study and constitute the entire manufacturing sector. See the data Appendix for further details.

Table 1 (a). The response of the change in profit rate to the lagged value of the profit rate, all manufacturing sectors.

	OLS (1)	FE (2)	OLS (3)	FE (4)	OLS (5)	FE (6)
Intercept	2.727*** (0.446)	5.609*** (1.279)	2.881*** (0.472)	5.739*** (1.220)	–2.871 (3.414)	–2.214 (4.256)
Rt–1 (lagged profit rate)	0.926*** (0.015)	0.851*** (0.033)	0.926*** (0.016)	0.852*** (0.031)	0.923*** (0.020)	0.843*** (0.034)
2009 dummy			–5.037** (1.669)	–4.935** (1.626)	–4.467* (1.828)	–4.126* (1.765)
Average profit rate					0.162 (0.102)	0.229 (0.122)
Observations	532	532	532	532	532	532

* p < .05.

** p < .01.

*** p < .001

Table 1 (b). The response of the change in profit rate to the lagged value of the profit rate, excluding the Petroleum and coal products secto.r.

	OLS (1)	FE (2)	OLS (3)	OLS (4)	FE (5)	FE (6)	OLS (7)	FE (8)
Intercept	3.345*** (0.736)	5.406* (2.199)	3.584*** (0.731)	3.791*** (0.737)	5.716* (2.154)	5.941* (2.168)	–1.411 (2.529)	–2.499 (2.734)
Rt–1 (lagged profit rate)	0.901*** (0.019)	0.845*** (0.060)	0.899*** (0.019)	0.898*** (0.019)	0.841*** (0.058)	0.840*** (0.059)	0.891*** (0.019)	0.818*** (0.066)
2009 dummy			–4.643* (1.708)	–4.833* (1.717)	–4.799* (1.738)	–4.991* (1.743)	–4.291* (1.833)	–4.100* (1.851)
2002 dummy				–5.091*** (1.314)		–5.128*** (1.268)	–4.010** (1.278)	–3.305* (1.254)
Average profit rate							0.149* (0.065)	0.253** (0.075)
Observations	504	504	504	504	504	504	504	504

* p < .05.

** p < .01.

*** p < .001

Table 2. The proportional change in investment, in response to the lagged profit rate.

	OLS (1)	OLS (2)	OLS (3)
Intercept	−0.000608 (0.00562)	−0.00456 (0.00945)	0.00302 (0.00994)
Rt–1 (lagged profit rate)	0.00108*** (0.00016)	0.00122*** (0.00030)	0.00119*** (0.00030)
2009 dummy			−0.0721* (0.031)
2002 dummy			−0.108*** (0.019)
Petroleum and coal products sector	Yes	No	No
Number of observations	551	522	522

* p < .05.

**p < .01.

***p < .001.

Table 3. Percentage investment flow change by year.

Year	1987	1988	1989	1990	1991	1992	1993	1994	1995
β^R	− 0.05	− 0.01	− 0.01	0.08	0.34	0.07	− 0.01	0.29	− 0.05
1996	1997	1998	1999	2000	2001	2002	2003	2004	2005
− 0.14	0.09	0.25	− 0.05	0.15	0.52	0.16	− 0.12	0.26	− 0.02
2006	2007	2008	2009	2010	2011	2012	2013	2014	2015
0.28	0.07	0.17	− 0.09	− 0.42	0.33	0.32	− 0.34	− 0.10	0.00

The categories used in compiling the data do not necessarily correspond perfectly with theory, which involves theoretical concepts appropriate to its own domain (Stigler 1963). The issues include the deviation of historical and replacement costs; the impact of high inflation on the historic cost of capital, with older assets being less expensive in nominal terms and therefore artificially associated with a higher rate of return; the omission of the ‘wages’ of the owners of small businesses, in sectors where such firms are predominant; and the omission of noncorporate businesses from the data. Depreciation is likely to have varied between industries and over time. The same is true of taxation. These are likely to have introduced non-differential measurement error. Furthermore, there are controversies over the correct calculation of capital and land, and over the measurement of goodwill and whether it is depreciated. To the extent that these generate non-differential measurement error bias, they would have a diluting effect, making it more difficult to obtain clear-cut findings.

The analysis covered manufacturing only. Additional issues would arise if services were included. For example, inspection of the data revealed that Legal services had profit rates in the range 271.6 to 376.0%, far in excess of any manufacturing sector. In such a case, capital in the usual sense probably plays a rather minor role in the cost structure, which is primarily driven by expertise (Biery 2015), undermining the use of fixed assets as the (sole) denominator. In addition, small service firms often rent the capital necessary for production, rather than purchasing capital goods. These expenditures are counted as intermediate consumption in the firm’s accounting system (Görzig and Gornig 2013). The inclusion of services would clearly add extra sources of heterogeneity, making interpretation difficult.

5. The range of observations and their implications for theory

The data allow the following types of observation to be made. These can be used to evaluate each of the theoretical propositions outlined above from an empirical viewpoint.

5.1. The profit rate distribution

According to pure neoclassical theory, at equilibrium there should be a single economy-wide rate of return on capital, with minimal dispersion. In practice, however, it is likely that deviations would be observed, due to factors described above. In addition, shocks could lead to further divergence, temporarily at least.

The most informative measures are the standard deviation/variance/coefficient of variation and the skewness of the profit rate distribution. Trends in the variance provide evidence on convergence or divergence, and the degree of skewness favours some of the theoretical propositions over others, as previously noted.

In addition, measurement error can occur giving the false impression of dispersion. If non-differential, the resulting dispersion would be symmetric.

5.2. Industry-specific movements

As part of the examination of heterogeneity, it is possible to observe the trajectories of each industry over time. This could provide some preliminary indication that industry-specific innovations or shocks are present. However, additional information would be needed to illuminate the nature of any such change. This complementary evidence could be quantitative and/or qualitative.

In addition, the pattern of industry-specific movements could provide some information relevant to the possible hypotheses outlined earlier. For example, some of them might be expected to produce differences in profit rates that vary little over time, including Inter-industry differences in monetary or non-monetary rewards.

5.3. Impact of macro shocks

Due to the panel structure of the dataset, the effects of macro-level shocks would be visible as a change in dispersion following a known macroeconomic event, after a suitable lag period. During the period covered by this dataset, the obvious candidates are NAFTA, which came into force in 1995, the dot-com bubble and crash at the turn of the century, China’s accession to the WTO in 2001 and the accompanying change in US trade policy (Pierce and Schott 2016), and the financial crisis of 2007-09.

5.4. Convergence

It is possible to test both for σ- and β- convergence using these data, by analogy with the literature on economic growth. Here, σ denotes the standard deviation of the rates of return, and β indicates the regression coefficient when the profit rate is regressed on its lagged value.

5.5. Response of investment to the profit rate

By regressing the quantity of investment on the lagged profit rate, the sensitivity of inter-industry flows to heterogeneous profitability can be assessed. This provides an indication of the degree of fluidity (interchangeability) of capital between sectors.

5.6. Impact of the quantity of capital on its rate of return

Similarly, the rate of return can be regressed on the lagged quantity of capital. This gives information on the presence of diminishing returns.

6. The observed profit rate distribution

The rate of return is calculated as the Gross Operating Surplus for each sector in each year, divided by the Fixed Assets for the previous year, expressed as a percentage. A lag is appropriate because the profit is realised after the investment has been made. The results presented here are for a one-year lag. Sensitivity analyses (not presented) show that the use of other lag structures, for example the average of three or five years, makes little difference. In addition, the use of a one-year lag enables a longer time series to be included.

In order to visualise the distribution of the rates of return, the data for all years, as well as for all sectors, were pooled. With more than 500 observations, a stable distribution was thus obtained, which can be characterised quite precisely.

The mean profit rate was estimated as 38.7%, with a median of 35.9% (Figure 1, panel (a)). This difference suggests right-skewness, which is confirmed by a skewness statistic of 2.2. The standard deviation was 18.9%, and the coefficient of variation was 0.49. The kurtosis was 8.5. The number of observations lying outside the range 25 to 50% was 198 (35.9%).

Figure 1. The observed profit rate distribution in US manufacturing sectors, 1987–2015 (pooled), for all manufacturing sectors (panel a), and for all manufacturing sectors, excluding Petroleum and coal products (panel b) (the reason for this is given in the text – see section on Descriptive statistics).

Inspection of the time course for each of the sectors indicated that one particular sector, Petroleum and coal products, was an extreme outlier (see next section). After exclusion of this sector, the distribution appeared more symmetrical (Figure 1, panel (b)): the mean was now estimated as 36.6%, with the median little changed at 35.2%. The skewness was now only 0.9. The standard deviation was 14.5% and the coefficient of variation 0.40. The kurtosis was now down to 1.7. The number of observations lying outside the range 25 to 50% was 178 (34.1%).

7. Profit rate movements over time

7.1. Descriptive statistics

The evolution of the profit rate for all manufacturing sectors is shown in Figure 2(a). The most striking feature is that one sector, Petroleum and coal products, is very different from all the other sectors: from early in the twenty-first century, its profits rose sharply to a level quite outside the range of the other sectors, reaching 158.6% in 2005 and staying above 80% for the succeeding ten years. This corresponds to a large rise in the crude oil price at that time.²

Figure 2. The evolution of profit rates by sector, 1987–2015, for all manufacturing sectors (panel a), and for all manufacturing sectors, excluding Petroleum and coal products (panel b). Note their different vertical axes.

It is therefore prudent to examine the behaviour of the profit rate after excluding this outlying sector. The sensitivity of the analysis of convergence to such a course of action was assessed by repeating the analysis after sequential removal of each of the next most profitable three sectors (Apparel and leather and allied products; Furniture and related products; Food and beverage and tobacco products). Only the exclusion of Petroleum and coal products had a major impact on the findings (details available on request).

The profit rates for all the remaining sectors are shown in Figure 2(b). Considerable dispersion is visible, especially in the period up to the year 2000. Supra-normal profits are observed in two sectors, Apparel and leather and allied products and Furniture and related products, during the early part of the period covered. The degree of dispersion and the mean rate of return both diminish over time (evidence available on request).

The position of individual industries is subject to considerable variation. Apparel and leather and allied products starts with the highest rate, but declines in the second half of the 1990s and the 2000s, ending with the lowest rate. Furniture and related products starts high, plunges to mid-range after 2006, then rises again in the 2010s. At the other end, Primary metals starts with the lowest profit rate and stays low, apart from a surge in 2004 through 2008. In general, sharp year-to-year volatility is not a dominant feature; rather, industries tend to maintain their relative position for several years, or even a decade or more, often without any obvious reason for this, for example a technical change or a new product.

The impact of the financial crisis is clearly evident, with a large dispersion in 2009. This is largely due to a fall in profitability of Motor vehicles, bodies and trailers, and parts, and a rise for Food and beverage and tobacco products, with most industries not showing any obvious effect (Figure 2(b)). The recovery is immediate: by 2010 the degree of dispersion visible is no longer increased. This is statistically confirmed by the variance returning to within the normal range. No other macro shocks are clearly visible, for example of NAFTA, the dot-com boom and crash, or China’s accession to the WTO.

7.2. σ-convergence

Figure 3 shows the evolution of the variance over time, together with a linear regression line corresponding to the equation

(1) ${\sigma }^2={\alpha }_{\sigma }+{\beta }_{\sigma }\mathit{t}$(1)

Figure 3. The variance of the profit rate over time, for all manufacturing sectors (panel a), and for all manufacturing sectors, excluding Petroleum and coal products (panel b). Note their different vertical axes.

where σ² is the variance of the profit rate, t is time, and α_σ and β_σ are parameters to be estimated.

In panel (a), there is a large departure from the previous range of values, starting in 2003. The regression line shows an upward trend. After exclusion of the Petroleum and coal products sector (panel (b)), a much lower degree of volatility is observed, and a clearly downward trend over time.

Thus, the impression of convergence from Figure 2(b) is confirmed. Again, the impact of the financial crisis is visible in 2009, and by 2010 the variance of profit rates is down to just below the regression line.

The speed of convergence, while large, was not observed to have brought about a single rate of return on capital across all of manufacturing. At the end of the study period, the rates still varied from 17.0% (Apparel and leather and allied products) to 51.6% (Food and beverage and tobacco products) – even without the Petroleum and coal products sector, which was over 80%.

7.3. β-convergence

Beta-convergence implies that the change in profit rate in a particular year is a negative function of the level in the previous year. A relatively high rate will tend to be followed by a fall, and a low rate will be followed by a rise. This can be expressed in the following equation, in which a negative value of β^C indicates convergence.

(2) $\mathrm{\Delta R}\mathit{\hspace{0.17em}}=\mathit{\hspace{0.17em}}{R}_{\mathit{it}}-R_{\mathit{i},\mathit{\hspace{0.17em}}t-1}={{\alpha }^C}_{\mathit{t}}+{{\beta }^C}_{\mathit{t}}{R}_{\mathit{i},\mathit{\hspace{0.17em}}t-1}+{\gamma }^C{X}_{\mathit{it}}+{{\in }^C}_{\mathit{it}}$(2)

where R is the rate of return on capital, and X is a vector of covariates; α^C, β^C and γ^C are parameters to be estimated, and ϵ^C is the error term.

This can be rearranged as

(3) $R_{\mathit{it}}={{\alpha }^C}_{\mathit{t}}+\mathit{\hspace{0.17em}}\left(1\mathit{\hspace{0.17em}}+{{\beta }^C}_{\mathit{t}}\right)R_{\mathit{i},\mathit{\hspace{0.17em}}t-1}+{\gamma }^C{X}_{\mathit{it}}+{{\in }^C}_{\mathit{it}}$(3)

Convergence could be to a common rate, or to a sector-specific rate. Accordingly, this equation was estimated using both Ordinary Least Squares and Fixed Effects regression. This approach follows the method of panel convergence used in the literature on economic growth. Robust standard errors were used for all regression analyses. The results are shown in Table 1(a) for all sectors, and Table 1(b) after exclusion of Petroleum and coal products.

Both tables show highly significant β-convergence. Focusing on Table 1 (b), the rate of convergence is 9.9% (100*(1–0.901)) for OLS, and 15.5% (100*(1–0.845)) for FE. When individual-sector intercepts were included in the FE regression (data not shown), the robust test using Welch’s F-statistic was far from significant, with p = 0.80. The time variation was not large, with only 5 out of 27 years being significantly different at the 5% level; addition of the two largest deviations, 2002 and 2009, as dummy variables scarcely altered the main findings. When the average profit rate was added in addition, the estimate of β^C in the OLS regression was 10.9% (95% CI 7.2, 14.6), and that in the FE regression was 18.2% (95% CI 5.3, 31.1). Convergence to the all-manufacturing mean rate was 14.9% (95% CI 2.2, 27.6) for the OLS analysis, and 25.3% (95% CI 10.6, 40.0) for the Fixed Effects analysis.

The results when all sectors were included (Table 1 (a)) were similar: the estimates of β^C were respectively 7.4 and 14.9% for OLS and FE, and Welch’s F-statistic gave a value of p = 0.97. With addition of the average profit rate, the estimates of β^C scarcely altered to 7.7 and 15.7%. The estimate of the magnitude of convergence to the all-manufacturing mean rate was similar to that obtained when the Petroleum and coal products sector was omitted, but the standard error was far higher, so that in this case it was not significant.

The Schwarz criterion, with Petroleum and coal products excluded, was 3189.263 for the pooled OLS regression, 3277.708 for the FE regression, and 3373.589 for the FE regression when time dummies were included. This clearly indicates that the OLS regression is the preferred analysis. It means that the sectors are all converging to a single common rate of return, not a sector-specific rate. Taking column 4 of Table 1 (b) as the definitive analysis, this common rate of return is given by α^C/(1 – β^C) = 3.791/(1–0.898) = 37.2%.

8. Response of investment to the profit rate

A standard proposition in economic theory is that investment should flow towards the more profitable sectors (and firms), and away from those that are less profitable. This can be expressed in the following equation, in which the proportional change in investment depends on the rate of return in the previous year:

(4) $\mathrm{\Delta }\mathit{I}/I_{\mathit{i},\mathit{t}-1}=\mathit{\hspace{0.17em}}\left(I_{\mathit{it}}-I_{\mathit{i},\mathit{t}-1}\right)\mathit{\hspace{0.17em}}/I_{\mathit{i},\mathit{t}-1}={{\alpha }^R}_{\mathit{t}}+{{\beta }^R}_{\mathit{t}}{R}_{\mathit{i},\mathit{\hspace{0.17em}}t-1}+{\gamma }^R{X}_{\mathit{it}}+{{\in }^R}_{\mathit{it}}$(4)

(where I is investment in private fixed assets).

The findings are shown in Table 2. The estimate of the coefficient is 0.0011 for the whole sample. After exclusion of the Petroleum and coal products sector, the coefficient is 0.0012 for the whole sample, both with and without the dummies for 2002 and 2009. This means that for a one percentage point change in profit rate, for example from 38.0% to 39.0%, the percentage change in investment is 0.12% (95% Confidence Interval 0.06, 0.18).

In addition, a more disaggregated set of regression analyses was carried out to show the response of investment to the profit rate in different sectors for each year (Table 3). The findings fluctuate markedly from year to year. The expected positive relationship is seen slightly more often (15) than a negative one (13). Positive coefficients greater than 0.2 are more frequent (8) than negative ones less than −0.2 (2). There is no obvious clustering of years with respect to the direction of flows, nor any obvious impact of major macro events such as NAFTA, the dot-com bubble and crash, China’s accession to the WTO, or the financial crisis and ensuing great recession. One can therefore say that investment is attracted to the more profitable sectors, but only in an irregular fashion. Clearly other causes are operating as well.

Table 4 shows the response of investment to the previous year’s rate of return, separately for each sector across the whole period of study. Almost all the coefficients are positive, some strongly so. Only four sectors had negative coefficients, with substantially negative values for Food and beverage and tobacco products, and for Printing and related support activities. Within most sectors, therefore, a higher profit tends to be followed by more investment in the following year.

Table 4. Percentage investment flow change by sector.

Sector	β^R
Wood products	0.76
Nonmetallic mineral products	0.43
Primary metals	0.49
Fabricated metal products	0.06
Machinery	0.40
Computer and electronic products	0.77
Electrical equipment, appliances, and components	0.35
Motor vehicles, bodies and trailers, and parts	− 0.02
Other transportation equipment	− 0.08
Miscellaneous manufacturing	0.20
Textile mills and textile product mills	0.25
Paper products	0.92
Printing and related support activities	− 0.33
Chemical products	0.77
Plastics and rubber products	0.48
Food and beverage and tobacco products	− 0.49
Apparel and leather and allied products	0.09
Petroleum and coal products	0.13

9. Impact of the quantity of capital on its rate of return

Neoclassical theory proposes that as more capital accumulates, its rate of return will inevitably decrease – the hypothesis of diminishing returns. The magnitude of this effect can be estimated as a regression of the profit rate on the lagged quantity of capital:

(5) $R_{\mathit{it}}={{\alpha }^I}_{\mathit{t}}+{{\beta }^I}_{\mathit{t}}{K}_{\mathit{i},\mathit{\hspace{0.17em}}t-1}+{\gamma }^I{X}_{\mathit{it}}+{{\in }^I}_{\mathit{it}}$(5)

(where K is fixed assets).

The regression coefficient was found to have the expected negative sign, but it was not significant and its magnitude was small (Table 5). Excluding the Petroleum and coal products sector, in which the very high profit in the latter part of the period may have diluted the effect, the largest estimate (without the year dummies for 2002 and 2009) was that for each billion dollars invested, the rate of return decreases by 0.0081% (95% CI −0.0400, +0.0239). It is essentially zero.

Table 5. The response of the profit rate to the lagged quantity of capital.

	OLS (1)	OLS (2)	OLS (3)
Intercept	39.14*** (3.53)	37.34*** (3.17)	37.74*** (3.21)
Ki, t–1 (lagged fixed capital quantity)	−0.00519 (0.0159)	−0.00806 (0.0163)	−0.00740 (0.0161)
2009 dummy			−7.28* (3.28)
2002 dummy			−5.84*** (1.42)
Petroleum and coal products sector	Yes	No	No
Number of observations	551	522	522

* p < .05.

**p < .01.

***p < .001.

10. Discussion

10.1. Strengths and limitations

In contrast with some of the early literature on this topic, no assumption was made concerning the predominant causal factor that might explain any observed dispersion or asymmetry in the profit rate distribution, such as market power. Rather, the approach taken here is an exploratory (‘data-first’) analysis, providing a robust statistical description of the profit rate distribution at industry level. It assumes that multiple causal processes may be operating, and seeks to document what has actually occurred before attempting to attribute the findings to specific causes. As far as I have been able to ascertain, the existing literature does not contain such an analysis. Section 10.2 discusses the theories described in section 2 in the light of these findings.

The dataset allows an analysis that covers the years from 1987 to 2015. This is a sufficiently long period to allay the worry that the findings could be distorted by business-cycle fluctuations. It also covers the implementation of NAFTA, the dot-com bubble/crash and China’s accession to the WTO, as well as the financial crisis. Effects of some of these macro shocks were detectable in the econometric analysis, but inclusion of the relevant year dummies did not affect the main findings, and the disturbances attributable to these events were remarkably transient. In fact, the major time-related disturbing factor was the trajectory of the profit rate of the Petroleum and coal products sector in the second part of the period covered (which could easily have been missed if the sector-specific time series had not been visualised). This was associated with the more than quadrupling of the global crude oil price at that time. Its exclusion altered the findings on σ-convergence and on skewness, but not on β-convergence, response of investment to the profit rate, or diminishing returns.

The disadvantages of a crude measure such as gross operating surplus (GOS) are well known. It is a measure of the accounting rate of return, rather than the economic concept which focuses on the difference between that and the normal profit rate that prevails at any one time.

Accounting data can certainly be seriously in error when used to assess the return on an individual investment initiative by a particular firm, due to the time patterns in the returns to investment and in the depreciation schedule, and to inflation (Fisher and McGowan 1983). Such problems would tend to even out in the context of the present sector-level analysis and long timespan. In the current context, the main problem with the use of accounting data is that conservative accounting conventions tend to lead to the measured value understating the present value of future profits. Any resulting bias would mean that high (low) measured rates are overvalued (undervalued), so that any observed dispersion would tend to persist (Mueller 1990, 9–10). This implies that the present finding of substantial convergence is, if anything, underestimated.

In addition, non-differential measurement error occurs, e.g. due to year-to-year variation in the relationship between the growth rates of the measured capital stock and of the present value of future profits (Mueller 1990, 9). Such non-differential error would lead to attenuation of the findings on convergence, implying that the clear convergence reported in this paper would have been even more marked if a more accurate measure had been used.

On the other hand, if the measure of GOS used here is subject to unrecognised sources of systematic bias, this would be unlikely to explain the observed convergent trend, because that would require a sharp trend in the sources of bias. More likely is that the degree of bias in the profit rate estimates is relatively constant, and that the trend corresponds to an actual change in the economy.

10.2. Evaluation of the various theories

10.2.1. Dynamic theories

Penrose’s work was not primarily focused on profit rates, and provides less precise predictions than neoclassical theory for this analysis. I therefore extrapolate from her basic perspective, which emphasised agency, managerial capabilities, heterogeneity and open-endedness. It could be argued that any firm-centred and empirically-based analysis would inevitably highlight these four features, because they are core features of business in the real world – as would be clear to readers of the economic news.

These attributes predict a broad and persistent profit rate distribution, with no reason to expect a high degree of skewness at firm level. To the extent that industries differ in these respects, the same would apply at industry level. This corresponds well with the findings of this analysis.

The emphasis on agency and heterogeneous managerial/entrepreneurial ability would suggest that a divergent tendency would be more likely in especially dynamic economies. American manufacturing was particularly vibrant during the mid-twentieth century – its Golden Age – and this could explain Stigler’s finding of divergence during that period. It would suggest that the relative decline in US manufacturing in the later twentieth century would have been accompanied by an end to the divergent tendency (although Penrose’s theory does not predict convergence). This hypothesis is suggested tentatively, and would require further research to provide evidence on it.

One of Penrose’s important insights is that relatively large firm size and high profitability do not necessarily indicate monopoly power. Her attribution of relative success to ‘more able and enterprising managers and entrepreneurs’ (p. 164) corresponds to the unequal ex ante strength of different firms’ initiatives (investments), which depend on the firm’s resources and how well they are used. (Other factors, such as location and access to relevant human and natural resources could also influence this (Tsoul?dis and Tsaliki 2005).) A relatively high profit rate is therefore not necessarily an indicator of market power in the neoclassical sense; rather, it could result from superior managerial capability which could be seen as a different form of power, in the causal sense of the degree of ability to influence events.

Schumpeter, like Penrose, emphasised agency and its role in promoting change. In his case, initiatives were taken by entrepreneurial outsiders in Mark I of his theory, and by the innovative parts of established firms on the basis of R&D in Mark II. In both versions, innovation was assumed to be associated with higher profit rates, predicting a positively skewed distribution. In practice, the observed distribution was close to symmetrical.

Similarly, the industries with the highest profit rates at various periods other than Petroleum and coal products – Apparel and leather and allied products; Furniture and related products; Food and beverage and tobacco products – would be hard to characterise as ‘more advantageous’. Nevertheless, Schumpeter’s concept of entrepreneurial profit could readily be reformulated not as an excess over a normal rate, but rather in terms of a varying chance of success, which could well be symmetric.

As with Penrose, Schumpeter’s theory of entrepreneurial profit did not necessarily predict a systematic tendency to convergence in profit rates. And again, economies with more successful innovation might be expected to show more divergence, and vice versa.

10.2.2. Neoclassical theory

The neoclassical prediction that all industries (as well as all firms) should have a profit rate close to the standard rate of return was comprehensively refuted by the substantial and persistent profit rate dispersion – despite the conservative bias due to the use of the two-digit industry level, and the likely extent of nondifferential measurement error. There is no standard rate of return.

The magnitude of the dispersion at the start of the study period raises the question of the trajectory of profit rates before 1987. If the observed convergence rate were a permanent feature of the US economy, a simple extrapolation backwards in time would be appropriate. This would suggest that the dispersion in, say, the mid-twentieth century was even wider than the more than 7-fold ratio observed in 1987, and still more extreme if one followed the same trend further backwards in time. This is clearly absurd.

The implication is that a divergent force must have been present at some time before 1987. One possibility is that the degree of dispersion could have been brought about by one or more macro shocks. This is highly unlikely, because by far the largest shock since World War II was the 2007–09 financial crisis, and although its effects were clearly evident in the dispersion of profit rates in 2009, they had completely disappeared by 2010. There are no candidates for a macro shock that could have created a sustained dispersion.

Alternatively, there could have been a more gradual divergent force operating in the period before 1987, resulting from heterogeneous performances of specific industries and/or firms. In principle, this question could be explored by examining the previous empirical literature. If the studies of earlier periods had used comparable data and methods, a consistent analysis over a much longer timespan would have been possible. Unfortunately, as reviewed above, a number of different approaches were used, apart from the internationally comparable studies reported in Mueller (1990), so that direct comparability is not achievable. As previously argued, the evidence tentatively suggests divergence in the mid twentieth century, a short period of stability, and then convergence starting in the 1960s.

If neoclassical theory cannot explain the persisting dispersion, perhaps it can account for the convergence that did occur? – after all, convergence is the core of the theory. Even in this it is unsuccessful; the empirical analysis presented above indicates that this could not have been brought about by differential capital flows plus diminishing returns. The tendency to differential capital flows was observed to be weak, and in this dataset at least, diminishing returns do not appear to exist. Entrepreneurs apparently stick to the line of business that suits their expertise, even if this means accepting a lower rate of return.

This finding contradicts Stigler’s statement that ‘Entrepreneurs will seek to leave relatively unprofitable industries and enter relatively profitable industries, and with competition there will be neither public nor private barriers to these movements. … [without this] the immobility of resources would lead to catastrophic inefficiency’ (Stigler 1963, 54). The implication is that neoclassical theory of this kind misinterprets the fundamental nature of capitalist economic success: it does not result from flexibility bringing about a perfect market. Arbitrage between production systems with differing degrees of productivity and profitability may well play little or no role in capitalist dynamism. The important action is in production: a consequence of the investment initiatives of entrepreneurs and firms – dynamic rather than allocative efficiency (Shiozawa 2020).

The finding that diminishing returns did not occur is similar to that of Nell and Thirlwall (2017; 2018) in the context of the impact on GDP of national-level investment. It is remarkable that there is such a small empirical literature on such a fundamental and ubiquitous concept as diminishing returns to financial capital, and that the available evidence is against its occurrence.

This leaves the possibility that supra-normal profits are eroded by new entrants, thus returning the economy to a situation closer to the ideal of a uniform rate of return. This is discussed in the next section.

10.2.3. Deviations from standard neoclassical theory when its assumptions do not hold

The notion of market power as a factor that can increase the profit rate above the baseline of the competitive market, but not decrease it, contributes little to the inter-industry variation of profit rates, as shown by the symmetry of the distribution. The extent of churning observed in Figure 2 also suggests that the degree of dispersion is not due to a relatively stable feature such as the extent of market power. It is reminiscent of the churning observed in other contexts (e.g. Foster, Haltiwanger, and Syverson 2008) and ‘turbulent’ competition (Shaikh 2016). These usually refer to the firm level, but the evidence here is that it occurs also at industry level, possibly as a result of changing competitive conditions, e.g. lower priced imports.

New imports eroding supra-normal profits could explain the observed convergence. Apparel and leather and allied products and Furniture and related products were relatively profitable specifically in the early part of the study period. Globalisation in the late twentieth century may have forced US firms in these sectors to reduce their prices, and therefore their profits, to compete with less expensive imports. This price undercutting is compatible with neoclassical theory, but it does not require a sophisticated theory to predict that cheaper goods will tend to outsell expensive ones, ceteris paribus. Firms with lower unit costs can charge lower prices, without loss of profit margin, and are therefore in a more powerful position.

Neoclassical economists correctly emphasise that profitability must always be seen in relation to risk. If interpreted to mean that the baseline level of risk is zero for investments in the least risky industries and positive in the riskier ones, a positive skew would be present, but this is not observed. It is more likely that differential risk is symmetrical, and simply corresponds to the operation of uncertainty (‘luck’) in the outcome of any initiative.

Neglect of intangible assets is a factor that could possibly distort the observed profit rate in some industries. Again, the symmetry of the distribution argues against this as a major issue. Secondly, it is generally agreed that the importance of intangible capital has increased over time; the quantity of capital would therefore be increasingly underestimated, and the measured profit rate should therefore have increased over time. This is not what is observed. Thirdly, the industries that were found to have periods of relatively high rates of return (apart from Petroleum and coal products) were Apparel and leather and allied products, Furniture and related products, and Food and beverage and tobacco products. These industries do not have high levels of intangible assets, apart from advertising.

11. Conclusion

This paper makes the following contributions. It provides an analysis of all 19 US manufacturing sectors for the period 1985–2016 and is nationally representative. It demonstrates that the degree of profit rate dispersion implies that the concept of a standard rate of return has no counterpart in reality.

The symmetry of the distribution implies that the observed departures from neoclassical predictions are not due to market power or the neglect of intangibles, and that theories invoking risk and entrepreneurial profit need to be reformulated. The investigation of inter-industry flows in response to differential profitability is a major contribution to the empirical literature on diminishing returns; it demonstrates that they do not play a major role.

The statistical analysis was designed to impose no causal relations unless they could be empirically justified, to directly investigate what causal processes are compatible with the data. This is in contrast to much of the existing literature where it is often assumed that profit rate equalisation and/or diminishing returns ‘must be’ fundamental features of the economy.

The context of this analysis is the considerable qualitative research undertaken by Penrose, a large body of rigorous economic history by Chandler (e.g. Chandler 1977), and also Lee’s (1999) empirical examination of price setting. Their findings point in the same direction. Together they can be taken as an empirical basis to construct evidence-based causal theory.

The findings correspond closely with the expectations generated from Penrose’s perspective. They suggest the following account. Firms take initiatives. Their quality depends on the degree of managerial ability. But their achieved outcome, in terms of the rate of return, is not guaranteed, because the initiative is taken under conditions of risk – or more likely, Knightian uncertainty. In practice, attempts at innovation vary greatly in their degree of success: many fail altogether, and the rate of return even among those that survive can be lower than the prevailing rate as well as above it. There is thus a broad range of possible outcomes in terms of the profitability of the entrepreneurial initiatives.

At the macro level, this manifests as profit rate heterogeneity. It is brought about by uneven success, at both the firm and the industry level, not by shocks, as neoclassical theory requires. It suggests that in an economy with dynamic manufacturing, profit rates will diverge (ceteris paribus), and that convergence may indicate relative industrial stagnation.

This interpretation implies that success in business involves the degree of efficacy or relative strength of entrepreneurs, directors and managers – their ability to bring something about. This is one meaning, a specifically causal one, of the word ‘power’, with the implication that market power is not the only type of power that is relevant to the profit rate. Positive profits can occur without ‘imperfect competition’ or oligopoly, simply as a result of unequal managerial capacity, as is seen every day in the financial news: the existence of a relatively high (low) profit rate tends to reflect a relatively high (low) level of entrepreneurial and/or management ability involved in taking previous investment initiatives; or more accurately, the degree of success in making a profit reflects (albeit imperfectly) the quality of the business plan as manifest in the investments made – its ex ante strength. In addition, achieved profit can be regarded as a source of ex post strength, as it provides the resources that can be used to fund future investment, or for other expenditure that could improve the future position of the firm (Joffe 2015).

The relationship of these two types of power can readily be related to the concept of market power. In any market transaction, monopoly/oligopoly arises when there is only one supplier (or very few), or when the suppliers collude. Monopsony/oligopsony arise when this is true on the demand side. When there are many suppliers, their inequality implies a distribution of relative strength, the most powerful one ex ante being the one most successful in competing, e.g. due to ability to produce at lowest unit cost. Similarly, the inequality in profit outcome leads to heterogeneity in ex post strength.

Acknowledgements

I would like to thank Ciaran Driver, Andrew Kliman, Tony Thirlwall, Julian Wells, and especially Ron Smith for helpful advice and comments. No funding was received for this work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.

Notes

1. I am grateful to an anonymous reviewer for suggesting that this should be included.

2. The crude oil price rose from $25/barrel in 2002 to over $100/barrel before and after the 2007-09 crisis. This was due to increasing demand from China and other Asian countries, the invasion of Iraq, and possibly speculation in futures markets (Williams n.d.).

Appendix

Table

Data appendix Gross operating surplus is the amount remaining after the wage bill and taxes on production and imports less subsidies have been deducted from the total revenue. It includes corporate profits and proprietors’ income as well as depreciation, net interest, and business transfer payments (Bureau of Economic Analysis 2011). Thus, it is a relatively rough measure of annual profit. The stocks of fixed assets include estimates of durable equipment, structures and software, using the perpetual inventory method (Bureau of Economic Analysis, 2003). This cumulates past investment flows to indirectly estimate the value of the stock, calculating the net stock in each year as the cumulative value of gross investment through that year less the cumulative value of depreciation through that year. The Bureau of Economic Analysis assumes that most assets have depreciation patterns that decline geometrically over time, an assumption that has strong empirical support, although the actual depreciation rates are of uncertain accuracy. The data come primarily from the economic censuses conducted every five years by the Bureau of the Census, the Annual Survey of Manufactures, and the Annual Capital Expenditures Survey (e.g. for software). New non-residential structures are derived from the National Income and Product Accounts (NIPA); all the data sources are reconciled with NIPA data (Bureau of Economic Analysis, 2019). Data collected on the historical-cost basis were used in this analysis. BUREAU OF ECONOMIC ANALYSIS. Fixed Assets and Consumer Durable Goods in the United States, 1925–99. Washington, DC: U.S. Government Printing Office, September, 2003. https://www.bea.gov/system/files/methodologies/Fixed-Assets-1925–97.pdf BUREAU OF ECONOMIC ANALYSIS. (2011). Measuring the nation’s economy: an industry perspective https://www.bea.gov/sites/default/files/methodologies/industry_primer.pdf BUREAU OF ECONOMIC ANALYSIS. NIPA Handbook 2019, chapter 6 on Private Fixed Investment https://www.bea.gov/system/files/2019-05/Chapter-6.pdf Sectors covered by the data Wood products

Nonmetallic mineral products

Primary metals

Fabricated metal products

Machinery

Computer and electronic products

Electrical equipment, appliances, and components

Motor vehicles, bodies and trailers, and parts

Other transportation equipment

Furniture and related products

Miscellaneous manufacturing

Food and beverage and tobacco products

Textile mills and textile product mills

Apparel and leather and allied products

Paper products

Printing and related support activities

Petroleum and coal products

Chemical products

Plastics and rubber products