Real Competition and Profit Rate Equalisation: Theory and Evidence from the Norwegian Economy

Abstract

The existence of long-run profitability differentials in market economies is a fundamental question that all traditions of economic thought since the times of the classical economists have dealt with in some form or another. In consideration of the modern synthesis of the classical views on competition into what has come to be known as the Theory of Real Competition, this article presents both a consistent theoretical basis from which to argue in favour of the tendential elimination of profitability premia across industries, as well as empirical evidence pointing to such conclusion from the Norwegian economy. The data, which covers 26 industries across nearly five decades (1971–2017), is used to estimate average and incremental total long-run profit rate differentials following two distinct methodologies. The first method has been commonly used in the prior literature, and the second has been newly systematised by this study’s author. Both methods are critically scrutinised, and their results compared to allow for a more robust conclusion. The findings suggest that average profit rates exhibit a weak tendency towards equalisation in Norway, and that such tendency is much stronger for incremental profit rates.

Main article text

1. Introduction

The question of whether there exists a tendency for profitability differentials across industries to disappear lies at the heart of the theoretical postulates on competition made by all major schools of economic thought that have studied the nature and functioning of market economies. In fact, most of these schools have either the affirmative or the negative position embedded into their theoretical corpus, even as its relevance may oftentimes be neglected or eclipsed by conclusions reached at higher analytical stages. What is more, the terms on which such proposition is accepted or rejected, as well as its theoretical characterisation, differ considerably across these schools, thereby making it of utmost importance for economists of all traditions to think carefully and critically about this question with the aim of attaining a description of the processes leading to the existence, or lack thereof, of differences in profitability across economic sectors that is realistic and informed by the empirical patterns observed in the data.

This work defends the answer to such a question provided by the modern synthesis of the classical insights into competition developed by Shaikh (2016) and provides empirical evidence in its support of the Norwegian economy, which, to such end, has notably been understudied. Norway possesses a highly advanced economy ranked among the best performing in the world on all major economic indicators. The Norwegian economy is also well-known for containing numerous state-owned enterprises, which have at times been accused of having anti-competitive advantages over their privately owned counterparts (OECD 2003, 24–28). Nevertheless, this economy is generally regarded as being highly liberalised and market-oriented, thus making it a great subject for the empirical inquiry into the issues of competition and profit rate equalisation.

In addition, this study systematises a novel methodology for ascertaining the existence of long-run profitability premia across industries primarily focused on, but not limited to, the Autoregressive Distributed Lag (ARDL) modelling approach to cointegration analysis proposed by Pesaran and Shin (1995), which overcomes some of the deficiencies of, and whose results can be directly compared to those of, what is arguably the most common methodology employed in the literature.

The remainder of the study is structured in the following manner: Section 2 contains a literature review of the main empirical works on this subject to this day. Section 3 discusses contending theoretical approaches to competition together with their stances on profit rate equalisation and advances the Theory of Real Competition as the most adequate. Section 4 presents the AR(1) methodology to test for the existence of profitability differentials across industries, which, being among the most used in the literature, is the first of the two econometric approaches used in the study. Section 5 develops the second econometric approach used to such end, grounded on more modern long-run modelling techniques. Section 6 presents and discusses the evidence on the equalisation of average rates of profit. Section 7 looks at the evidence on incremental rates of profit, which, as argued throughout the article, possess different properties to their average counterparts. Finally, Section 8 concludes the study by summarising the main arguments made throughout, as well as the most notable findings.

2. Empirical Literature Review

The empirical studies on the question of profit rate equalisation have thus far been primarily focused on its theoretical consequences, since many macroeconomic theories are premised on the existence of a competitive profit rate that is homogeneous across economic sectors, although relevant policy implications pertaining to competition and anti-trust laws could also be derived from their findings. However, the theoretical and methodological frameworks from which this subject has been empirically analysed differ considerably throughout the literature, making it notably difficult to gather all the results into a single, cohesive narrative. Such is, nonetheless, the aim of this section, which covers the developments made in the question’s specification and the sophistication of the econometric tools used in the major empirical works, as well as the main findings.

The first systematic empirical inquiries into this subject can be dated back to the 1950s and 1960s. ¹ They employed static, cross-sectional linear models that took an industry’s rate of profit at a given point in time (or the average across a short time span of 3–4 years) as the dependent variable and used as explanatory variables certain factors related to the state of competition in the industry, such as a measure of the degree of concentration. The hypothesis of profit rate equalisation was then expressed as the proposition that the parameters associated with such explanatory variables are not statistically different from zero. Their findings were taken to demonstrate the existence of uncompetitive profitability differentials. Nevertheless, these works are now mostly considered to be fundamentally flawed, the main reason being that their methods and evidence are not appropriate to determine the existence of systematic, long-run differences in profitability across economic sectors due to structural anti-competitive forces and could at most be said to only reflect short-run distortions.

The empirical examination of long-run profitability differentials then found a breakthrough in the 1970s and 1980s with the studies of the Austrian economist Dennis Mueller, ² who introduced the time-series econometric techniques that would go on to dominate the field. The most popular of these became the autoregressive models of first order (AR(1)), which had two distinct uses: the first of these was to model an industry’s profit rate at a given point in time as the sum of a time-invariant homogenous competitive rate, an industry-specific long-run premium and a time-varying short-run premium. The autoregressive process is then applied to each industry’s profit rate, from which an estimate of the sum of the two time-invariant components is obtained and compared across industries, the hypothesis of profit rate equalisation being then expressed as the inter-industry equality of such sums. This approach was, however, criticised for being incapable of estimating separately the long-run premium from the competitive profit rate, and for making the highly unrealistic assumption that such competitive rate is constant through time. The second application of the AR(1) process, which is the one used in this study, overcomes these issues by focusing on the time series of the difference between each industry’s profit rate and the economy’s mean profit rate, the latter being interpreted as the competitive rate. Modelling these difference series as AR(1) processes then allows the researcher to estimate the long-run profitability premium specific to each industry, as well as to test its statistical significance. For this reason, the second approach became the more commonly used of the two.

Among the countries where Mueller’s methods (or a variation of them) have been applied, we find the United States (Glick 1985; Glick and Ehrbar 1988, 1990; Kessides 1990; Gschwandtner 2005; Cuaresma and Gschwandtner 2008), Japan (Odagiri and Yamawaki 1990; Maruyama and Odagiri 2002), Greece (Lianos and Droucopoulos 1993), Canada (Khemani and Shapiro 1990; Rigby 1991), Germany (Schwalbach and Mahmood 1990), France (Jenny and Weber 1990), the United Kingdom (Cubbin and Geroski 1990; Goddard and Wilson 1996, 1999; McMillan and Wohar 2009), Turkey (Yurtoğlu 2004; Kaplan and Aslan 2008), and India (Kambahampati 1995). Studies have also been conducted using data from multiple countries (Geroski and Jacquemin 1988; Glen, Lee, and Singh 2001). Taken together, the results suggest that in all these countries there appear to be certain firms and industries that earn persistently higher (or lower) profits and have thus often been interpreted as the result of a lack of competition.

However, adopting as an analytical framework the theory of competition advanced in this article, it is argued that, since those studies consider either inter-firm or inter-industry profitability differentials without isolating the profitability conditions of the regulating capitals, which are theorised to be the ones subject to the forces of profit rate equalisation, their evidence cannot be said to reflect a lack of competition. Rather, such evidence is to be expected from the standard functioning of competitive economies. Shaikh (2008, 2016), following the classical economists and Marx, argues that within industries competition naturally produces a dispersion of profit rates across firms. Thus, if the profit rates of firms within an industry or the average profit rates of different industries within an economy were to be subjected to equalisation tests (as they are in the studies listed above) the results would unsurprisingly show that these rates do not get equalised, even in the long run. Nonetheless, Shaikh does argue, from both a theoretical and an empirical standpoint, that profit rate equalisation between industries takes place, only that instead of occurring at the level of average profit rates it occurs at that of incremental rates of return, ³ which approximate the profitability conditions of each industry’s regulating capital.

Studies applying Mueller’s methods to incremental rates of return have been produced for various economies (Christodoulopoulos 1995; Tsoulfidis and Tsaliki 2005, 2011; Vaona 2011; Bahçe and Eres 2012) and have mostly concluded that, whereas there does not appear to be a general tendency for average profit rates to get equalised, this tendency does exist and is remarkably strong for incremental rates of return.

Zacharias (2001) critiques the AR(1) approach to testing for-profit rate equalisation on the grounds that it does not discriminate between the component of each industry’s long-run premium that is directly related to the state of competition in the economy and the component that is only indirectly related to it. He develops instead a methodology based on the Johansen (1988, 1991) approach to cointegration analysis, from which he derives estimates of what he labels as the competitive and non-competitive components of the industry-specific total long-run differentials in the US manufacturing sector. Zacharias then interprets the hypothesis of profit rate equalisation as the statistical insignificance of the competitive component and finds that it cannot be rejected in 14 out of 20 industries. There is a brief description and usage of the ARDL methodology, but such an approach is neither systematised nor extended to allow for the computation of the industry-specific total long-run differential.

The problem with Zacharias’s interpretation is that by testing solely the significance of the so-called competitive differential, we are not accurately depicting the profitability premia that is due to the state of competition in the economy. In fact, since we are already considering long-run profitability premia, testing for the significance of the total long-run differential should suffice to ascertain the degree of profit rate equalisation in an economy due to the forces of competition. A better interpretation of Zacharias’s components would be to consider them as the dynamic and the non-dynamic components, where the dynamic component tells us how responsive each industry’s profitability is to the general state of profitability in the economy relative to the hypothetical scenario where it responds in a one-to-one manner, and the non-dynamic component depicts the part of an industry’s long-run profitability premium that is due to idiosyncratic factors not directly related to such general state of profitability, but that nevertheless are relevant in the assessment of the effects of competition on profitability differentials. ⁴ Thus, the hypothesis of profit rate equalisation is still to be regarded as the hypothesis of a statistically insignificant total long-run differential.

Considering the above, this work’s contribution to the literature consists of the following: first, the study is conducted on data from a highly relevant but understudied country, Norway. Second, the time span covered by the data (1971–2017) is among the largest, thereby allowing for consistent long-run inferences, and is the first to include observations beyond 2010. Third, the study systematises a novel empirical approach to the estimation of profitability differentials and compares the results to those of the most popular methodology employed to this day. Fourth, this article provides an improved interpretation of the distinct components forming the industry-specific total long-run profitability differential that can be identified with the novel method. Finally, the empirical examination of profit rate equalisation is carried out on both average and incremental rates of return, and therefore enables a more nuanced discussion pertaining to the effects of the competitive forces characteristic of market economies on the appearance or vanishing of differences in profitability across industries.

3. Real Competition, Regulating Capitals, and Profit Rate Equalisation

The dominant notion of competition in the contemporary neoclassical orthodoxy is that of perfect competition. ⁵ Under this paradigm, competition is famously treated as a state rather than a process. Such a state is characterised by the presence of an indefinite number of consumers and producers that is large enough to assure that no single agent has the power to move market prices away from their competitively determined level. The size of firms thus becomes crucial, since it is understood that the bigger a firm is and the larger its market share, the higher its uncompetitive price-setting power becomes. The perfectly competitive state also necessitates the economic profits of all firms to be fixed at the zero level in the long run so as to represent an equilibrium where no incentives exist for the entrance of new investors into, or the exit of older ones from, any given industry. As Jehle and Reny argue:

In a long-run equilibrium, we shall require not only that the market clears but also that no firm has an incentive to enter or exit the industry. Clearly, then, long-run profits must be non-negative . . . On the other hand, because all firms have free access to one another’s technology . . . no firm can be earning positive profits in the long run. (Jehle and Reny 2011, 168)

Furthermore, if constant returns to scale are assumed, the long-run competitive price is given entirely by the horizontal supply curve identified at the minimum point of the long-run average cost curve. This serves as the basis for the neoclassical version of the classical and Marxian price of production, since the neoclassical orthodoxy adds to the total average costs a homogeneous “normal” profit rate that represents the indirect (opportunity) cost of capital (Varian 1993, 387–388). Competition in this sense implies not only a strict equality of profit rates across firms and industries, but also an equality of market prices and their cost-determined competitive level.

The theory of perfect competition, however, is at best a theory on how competition would work in an ideal world, rather than a descriptive account of the actual functioning of competition in existing market economies, even as it is often employed in macroeconomic models of such economies. The lack of adherence to reality of this theory has led certain strands of the neoclassical school, as well as entire heterodox schools, such as the post-Keynesian and the neo-Marxian, to adopt instead some form of an imperfect competition theory. In these theories, firms differ in size and number across industries, thereby enabling some to set prices above their competitive level. Positive economic profits are thus expected to arise in some industries, producing a deadweight loss. The observed economic phenomena of market share concentration, unequal average profit rates, price-setting behaviour of firms, etc., instead of being ignored altogether, are then explained as deviations from the ideal, thereby giving these theories the appearance of empirical adequacy.

Nevertheless, both the perfect and imperfect approaches to competition are equally flawed insofar as they take as a point of reference the same mythological state. They thus incur the same mistake of conceptualising competition as perfect competition and explaining the real phenomena by appealing to a lack of it, rather than to the existence of competitive forces whose functioning lies outside of the false perfect–imperfect dichotomy.

In response to both approaches, Shaikh (2016, 259–326) synthesises the classical and Marxian insights into an alternative theory of competition, which he names the Theory of Real Competition. Under this account, competition is a war-like, turbulent, and chaotic process from which a certain order paradoxically emerges. Firms, rather than being passive price takers, are active price setters in a constant struggle to cut costs and outcompete each other. Profitability becomes the key regulating force informing capital movements and constantly driving firms in and out of business, thereby acting as the objective force determining the winners and losers of the competitive struggle. Furthermore, central to this theory is the notion that individual motives are continuously being overridden by social forces, shifting the focus from the optimisation problem of self-interested, hyperrational representative agents to the emergent social outcomes resulting from the interaction of heterogeneous economic agents. And although some of these outcomes may resemble those theorised in the perfectionist conception of competition, they are fundamentally distinct in nature, form, and implications.

Concerning the equalisation of profit rates, the Theory of Real Competition considers two analytical stages: the first is the stage of inter-firm competition within an industry, which produces a natural dispersion of profit rates across firms. The second stage deals with inter-industry competition within an economy, where profitability premia still appear at the level of each industry’s average profitability, but they become tendentially removed at that of their regulating capitals.

In the first stage, firms set prices aiming to attract the largest number of consumers possible. Since consumers will gravitate toward the lower prices, it is in the interest of these firms to cut costs (whether by decreasing wages, intensifying the working day, or innovating on more efficient production methods) so as to outcompete each other by lowering such prices while remaining profitable. ⁶ Such competitive force inflicts on prices of homogeneous commodities an equalising pressure, as the firms that cannot survive the price-cutting efforts of their competitors become extinct, and those that can survive end up selling cheaper too. This is, nonetheless, a tendential process, so at any given point in time there is expected to exist a distribution of prices of homogeneous commodities, albeit one where there is a prominent mode representing the dominant price. ⁷ In relationship to the earlier note on the dissimilarities between real and perfect competition, although this reasoning may on the surface look like that in the neoclassical Law of One Price, they nevertheless differ significantly, leading Shaikh (1980, 2016) to name the tendential equalisation of prices of homogeneous commodities the Law of Correlated Prices instead.

The first stage is also characterised by the acknowledgement of the distinction between firms and capitals, where the latter are conceived of as the plants in operation and their equipment. This distinction is highly relevant to the theory, since it is argued that “firms set prices but the operating conditions of capitals determine costs” (Shaikh 2016, 262). Thus, given the fact that, even if all other factors are kept equal, the set of capitals in an industry always differ at least in their vintage, and the newer capitals generally embody the more modern and least costly methods of production, competition is expected to result in a distribution of costs across an industry’s capitals. The direct implication of the first stage is then that competition naturally produces a systematic distribution of profit rates within an industry. The reason is that profit rates are functions of the per-unit profits and the capital intensity, and the per-unit profits are themselves functions of prices and costs. Thus, if a generalised tendency for prices of the same commodity to get equalised exists, but there is no such tendency for the costs of production and capital intensities, then there will not be an equalisation of profit rates within an industry.

In the second stage, the analysis is expanded to account for inter-industry competitive dynamics. Here, the analysis is centred around the profit-driven movements of new investments in and out of industries. These investments are directed toward a specific set of capitals of which two key features can be identified: first, they represent accessible methods of production (otherwise, if there were barriers to entry, the investments could not have been made). Second, they embody the least costly reproducible conditions, since among the set of possible methods of production, new investors will tend to adopt the more efficient (less costly) ones. The capitals in question are thus known as the regulating capitals representing an industry’s “best generally reproducible conditions of production” (Shaikh 2016, 265).

The argument then proceeds by establishing that, since the new investments are profit-motivated and directed toward the regulating capitals in every industry, the theoretical focus on the impacts of competition on profitability differentials should be placed on the profit rates earned on such capitals, rather than on each industry’s average profitability. ⁸ Industries with higher-than-average regulating rates of profit then attract increasing investment volumes, which, if sufficiently large, raise the growth of supply in the industry relative to that of demand, thereby putting downward pressure on prices and in turn bringing those profit rates down to the average. The opposite effect will be experienced by industries with lower-than-average regulating rates of profit, ensuring a tendential equalisation of these rates across industries. Such equalisation, rather than being an equilibrium state as in the theory of perfect competition, is a turbulent process in which profit rates never reach a stationary point where they are exactly equal, but instead are continuously gravitating around a moving competitive level. Only in the long run do the profitability differentials across regulating capitals tend to disappear, making it of utmost importance for empirical inquiries into this question to be conducted on samples covering large timespans, arguably of at least 20 years.

Thus, under this framework, evidence against the long-run equalisation of average profit rates is not considered as an indication of a lack of competition, but as the natural outcome of a competitive economy. Regulating rates of profit, however, are expected to be tendentially equalised. This study empirically examines both hypotheses in the Norwegian economy.

4. An AR(1) Approach to Testing for Profitability Differentials

The AR(1) approach utilised in this study begins with a simple model of the i^th industry’s long-run profit rate, ⁹ ${\pi }_{\mathrm{i},\mathrm{t}}^{*}$ , expressing it as the sum of two components: the time-varying average of all industry’s profit rates, π_t, and an industry-specific long-run premium, α_i; that is:

(1) $${\pi }_{\mathrm{i},\mathrm{t}}^{*}={\pi }_{\mathrm{t}}+{\alpha }_{\mathrm{i}}$$

The objective is now to estimate α_i consistently, for which we first define ${\mathrm{\pi }}_{\mathrm{i},\mathrm{t}}^{\prime }$ as the difference between the i^th industry profit rate and the economy-wide mean profit rate. Now, our model proposes that there is a convergence of ${{\pi }^{\prime }}_{\mathrm{i},\mathrm{t}}-{\alpha }_{\mathrm{i}}$ toward zero in the long run, yielding the following AR(1) specification:

(2) $$\left({{\pi }^{\prime }}_{\mathrm{i},\mathrm{t}}-{\alpha }_{\mathrm{i}}\right)={\beta }_{\mathrm{i}}\left({{\pi }^{\prime }}_{\mathrm{i},\mathrm{t}-1}-{\alpha }_{\mathrm{i}}\right)+{\epsilon }_{\mathrm{i},\mathrm{t}}\leftrightarrow {{\pi }^{\prime }}_{\mathrm{i},\mathrm{t}}={\alpha }_{\mathrm{i}}(1-{\beta }_{\mathrm{i}})+{\beta }_{\mathrm{i}}{{\pi }^{\prime }}_{\mathrm{i},\mathrm{t}-1}+{\epsilon }_{\mathrm{i},\mathrm{t}}$$

where ε_i,t is a white noise series with zero mean, and β_i is interpreted as the speed of convergence of the industry-specific profit rate deviation from the competitive rate to its long-run value, given by α_i. The closer that β_i is to zero, the faster is the convergence of short-run excess profits to their norm. An industry experiencing exceptionally high or low excess returns in the short run would thus feature a small β_i in a competitive economy.

The economically meaningful interpretation of the model, however, requires that |β_i| < 1, which is equivalent to saying that, for the AR(1) process to be appropriately applied, the difference series, ${{\pi }^{\prime }}_{\mathrm{i},\mathrm{t}}$ , of all industries must be stationary. Among the stationarity tests that could be conducted on any given difference series, Tsoulfidis and Tsaliki (2011) propose the non-linear Kapetanios–Shin–Snell (KSS) unit root test, ¹⁰ since our theory suggests that, given the turbulent nature of capital influxes in and out of industries in response to profitability differentials, the difference between an industry’s profit rate and the competitive profit rate will exhibit numerous non-linearities that may not be captured by the standard linear tests like the Augmented Dickey–Fuller (ADF) or the Philips–Perron (PP). If any of the difference series is found to be non-stationary, then it would have to be detrended prior to the estimation of the AR(1) model in Equation (2).

The constant (c = α_i (1 − β_i)) and slope (β_i) parameter of the AR(1) process can then be estimated by the Least Squares method, allowing the researcher to obtain an estimate of the i^th industry’s long-run profitability premium, ${\widehat{\alpha }}_{\mathrm{i}}$ , by taking the ratio of the estimated constant to $1-{\widehat{\beta }}_{\mathrm{i}}$ . Formal testing for the statistical significance of the long-run premia across industries, where the null hypothesis, H₀ : α_i = 0, is taken as the hypothesis of profit rate equalisation, can in turn be conducted. Such a task requires an estimate of the variance of the industry-specific long-run profitability differential, given by:

(3) $$\begin{array}{l}\mathrm{Var}\left({\widehat{\alpha }}_{\mathrm{i}}\right)\approx {\left[\frac{1}{1-{\widehat{\beta }}_{\mathrm{i}}}\right]}^2\mathrm{Var}\left({\widehat{\mathrm{c}}}_{\mathrm{i}}\right)+{\left[\frac{{\widehat{\mathrm{c}}}_{\mathrm{i}}}{{\left(1-{\widehat{\beta }}_{\mathrm{i}}\right)}^2}\right]}^2\mathrm{Var}\left({\widehat{\beta }}_{\mathrm{i}}\right)\\ +2\left[\frac{1}{1-{\widehat{\beta }}_{\mathrm{i}}}\right]\left[\frac{{\widehat{\mathrm{c}}}_{\mathrm{i}}}{{\left(1-{\widehat{\beta }}_{\mathrm{i}}\right)}^2}\right]\mathrm{Cov}\left({\widehat{\mathrm{c}}}_{\mathrm{i}},{\widehat{\beta }}_{\mathrm{i}}\right)\end{array}$$

5. The ARDL(p,q) Methodology and Its Variations

The AR(1) approach discussed in the last section, while allowing for an estimation of each industry’s total long-run profitability premium, does not discern between the part of the premium that is due to factors not directly related to the general profitability conditions in the economy, and the part that is due to how the industry-specific profit rate adjusts to movements in such general profitability conditions. Furthermore, the AR(1) process cannot be applied equally to deviation series that are stationary and non-stationary. This section thus develops an alternative econometric framework centred around, but not limited to, the ARDL approach to cointegration analysis advanced by Pesaran and Shin (1995) that addresses these limitations while allowing for an estimation of the total long-run profit rate differential in each industry.

We start by setting up a general ARDL(p, q) model relating the i^th industry’s average or incremental profit rate at some moment in time, π_i,t, to the mean of the other profit rates in the economy, π_t (referred to as the general profit rate henceforth): ¹¹

(4) $${\pi }_{\mathrm{i},\mathrm{t}}=\mathrm{c}+{\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{p}}({\beta }_{\mathrm{j}}\cdot {\pi }_{\mathrm{i},\mathrm{t}-\mathrm{j}})+{\displaystyle \sum }_{\mathrm{k}=0}^{\mathrm{q}}({\phi }_{\mathrm{k}}\cdot {\pi }_{\mathrm{t}-\mathrm{k}})+{ϵ}_{\mathrm{t}}$$

Subtracting π_{i, t−1} from both sides gives:

(5) $${\pi }_{\mathrm{i},\mathrm{t}}-{\pi }_{\mathrm{i},\mathrm{t}-1}=\Delta {\pi }_{\mathrm{i},\mathrm{t}}=\mathrm{c}+\left({\beta }_1-1\right)\cdot {\pi }_{\mathrm{i},\mathrm{t}-1}+{\displaystyle \sum }_{\mathrm{j}=2}^{\mathrm{p}}\left({\beta }_{\mathrm{j}}\cdot {\pi }_{\mathrm{i},\mathrm{t}-\mathrm{j}}\right)+{\displaystyle \sum }_{\mathrm{k}=0}^{\mathrm{q}}\left({\phi }_{\mathrm{k}}\cdot {\pi }_{\mathrm{t}-\mathrm{k}}\right)+{ϵ}_{\mathrm{t}}$$

Now, in a long-run equilibrium without shocks, there are two conditions that must be met: ∆ π_{i, t} = 0 and ϵ_t = 0. Under such conditions, Equation (5) results in:

(6) $$0=\mathrm{c}+\left[{\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{p}}\left({\beta }_{\mathrm{j}}\right)-1\right]\cdot {\pi }_{\mathrm{i}}+{\displaystyle \sum }_{\mathrm{k}=0}^{\mathrm{q}}\left({\phi }_{\mathrm{k}}\cdot \pi \right)$$

This expression can then be rearranged into:

(7) $${\pi }_{\mathrm{i}}=\frac{\mathrm{c}}{\left[1-{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}\left({\beta }_{\mathrm{j}}\right)\right]}+\frac{{{\displaystyle \sum }}_{\mathrm{k}=0}^{\mathrm{q}}\left({\phi }_{\mathrm{k}}\right)}{\left[1-{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}\left({\beta }_{\mathrm{j}}\right)\right]}\cdot \pi ={\gamma }_{\mathrm{i}}+{\theta }_{\mathrm{i}}\cdot \pi$$

where ${\gamma }_{\mathrm{i}}=\frac{\mathrm{c}}{\left[1-{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}\left({\beta }_{\mathrm{j}}\right)\right]}$ is the long-run constant and ${\theta }_{\mathrm{i}}=\frac{{{\displaystyle \sum }}_{\mathrm{k}=0}^{\mathrm{q}}\left({\phi }_{\mathrm{k}}\right)}{\left[1-{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}\left({\beta }_{\mathrm{j}}\right)\right]}$ the long-run coefficient associated with the general rate of profit.

To identify the total long-run differential between each industry’s profit rate and the general profit rate we proceed by subtracting π from both sides of Equation (7), yielding:

(8) $${\delta }_{\mathrm{i}}\equiv \mathrm{Total}\mathrm{Long}-\mathrm{Run}\mathrm{Differential}\equiv {\pi }_{\mathrm{i}}-\pi ={\gamma }_{\mathrm{i}}+\left({\theta }_{\mathrm{i}}-1\right)\cdot \pi ={\delta }_{\mathrm{i}}^{\neg \mathrm{d}}+{\delta }_{\mathrm{i}}^{\mathrm{d}}\cdot \pi$$

where ${\delta }_{\mathrm{i}}^{\neg \mathrm{d}}={\gamma }_{\mathrm{i}}\equiv$ non-dynamic differential, and ${\delta }_{\mathrm{i}}^{\mathrm{d}}=\left({\theta }_{\mathrm{i}}-1\right)\equiv$ dynamic differential.

This expression gives us the total long-run differential as a weighted combination of two components: first, the non-dynamic differential, whose weight is equal to one, represents the part of the total premium that is related to factors idiosyncratic to the industry in consideration but not directly related to the general state of profitability in the economy (i.e., risk, specific regulations affecting the industry, especial geographical location, etc.). Second, the dynamic differential, whose weight is equal to the long-run general rate of profit, accounts for the competitive adjustment of the industry’s profitability to the general state of profitability in the economy.

The key component of the dynamic differential is the long-run coefficient associated with the general rate of profit, θ_i, which represents the impact that a change in the general rate of profit has, in the long run, on the i^th industry’s profit rate. Thus, if the i^th industry’s rate of profit moves in a one-to-one fashion with the general profit rate, as would be expected of a competitive industry with a non-dynamic differential equal to zero, then the dynamic differential would also be equal to zero, and there would be no long-run profitability premia in the industry. If, however, the non-dynamic differential is negative (or positive), then the expected dynamic differential of a competitive industry is not equal to zero, but to a positive (or negative) number sufficiently large to offset the non-dynamic differential.

Therefore, the hypothesis of profit rate equalisation should not be expressed as the statistical insignificance of either one of the two components that form the total profitability premium, but as the statistical insignificance of the total long-run differential itself, since doing otherwise results in a high probability of rejecting the hypothesis of profit rate equalisation when such hypothesis is true or accepting it when it is false. For example, we can consider an industry which, by virtue of certain idiosyncratic factors, has a significant, negative non-dynamic differential. In a competitive economy featuring profit rate equalisation, such industry’s profitability would then have to increase by more than a one-to-one proportion with the general rate of profit to catch up with it, resulting in a combination between the dynamic and non-dynamic differentials where they cancel each other out, thereby eliminating the total long-run differential. The result, a statistically insignificant total differential, would then appropriately reflect the existence of a tendency for profit rates to get equalised. However, if we were to misidentify the hypothesis of profit rate equalisation as the statistical insignificance of either one of the total differential’s two components, our conclusion would be either that the industry features a negative premium (non-dynamic differential), or that it features a positive premium (dynamic differential).

The hypothesis directly drawn from the previous conclusion is that, in an economy where inter-industry rates of profit tend to get equalised, the dynamic and non-dynamic differentials should have opposite signs, and that the larger in absolute value one is, the larger in absolute value the other should be. Sections 6 and 7 provide empirical support for such a hypothesis on both average and incremental rates of profit.

However, before relying on the ARDL long-run coefficients, the existence of a long-run relationship between the i^th industry’s profit rate and the general profit rate must be established. To this end, the ARDL Bounds Test can be conducted. Here, the clear advantage that the ARDL approach to cointegration analysis has over the Johansen (1988, 1991) and the Engle and Granger (1987) approaches is that it does not require the non-stationarity of the profit rate series under consideration. The disadvantage is, nonetheless, that the ARDL coefficients can be relied upon only if the Bounds Test finds a unique long-run relationship between the two variables: either one where π_{i, t} is the regressand and π_t is the regressor, or one where π_t is the regressand and π_{i, t} is the regressor.

Thus, whereas a priori there is no need for a stationarity test to be conducted on any of the profit rates in the sample, since this procedure applies equally to stationary and non-stationary series, the stationarity tests should still be performed in the study of profit rate equalisation for two main reasons: first, because they allow the researcher to choose the appropriate bound to use as a reference for the rejection of the null hypothesis of no long-run relationship between the industry-specific profit rate and the general profit rate. Second, because if the Bounds Test does not provide sufficient evidence of a long-run relationship between such profit rates or concludes that more than one long-run relationship exists between them, and both rates are found to be non-stationary, the researcher can then use either the Johansen or the Engle and Granger procedure as alternatives. Of these two alternatives, this study adopts the Engle and Granger approach and produces estimates of the dynamic and non-dynamic differentials for those industries whose profit rates are cointegrated with the general rate of profit by means of the Fully Modified OLS estimation procedure.

Now, if the Bounds Test finds a unique long-run relationship between π_i,t and π_t where the former is the regressand and the latter is the regressor, then the estimates of the dynamic and non-dynamic differentials can be used to calculate the total long-run differential in accordance with Equation (8). Such a task, however, requires a proxy of the unobservable long-run general rate of profit. Here, given the fact that the general average and incremental rates of profit appear to fluctuate around a relatively stable point, thereby not showing any explosive behaviour, the decision was made to use the mean value of those series, $\overline{\pi }$ , as such proxy. The variance of the total differential is then given by:

(9) $$\mathrm{Var}\left({\widehat{\delta }}_{\mathrm{i}}\right)=\mathrm{Var}\left(\widehat{{\delta }_i^{\neg \mathrm{d}}}\right)+{\overline{\pi }}^2\cdot \mathrm{Var}\left(\widehat{{\delta }_i^{\mathrm{d}}}\right)+2\cdot \overline{\pi }\cdot \mathrm{Cov}\left(\widehat{{\delta }_i^{\neg \mathrm{d}}},\widehat{{\delta }_i^{\mathrm{d}}}\right)$$

In this expression, the variance of the dynamic and non-dynamic differentials can be straightforwardly estimated by means of the delta method, but the covariance between the two can be notably more cumbersome to compute. For this reason, such covariance was proxied with the covariance of the contemporary coefficients of the ARDL model. There is, however, expected to be only a slight difference between the long-run covariance and the contemporary covariance of such coefficients, since these covariances are typically very close to zero.

If, instead, the unique long-run relationship detected by the Bounds Test features π_t as the regressand and π_{i, t} as the regressor, then the total long-run differential would be given by:

(10) $$\begin{array}{l}{\delta }_{\mathrm{i}}\equiv \mathrm{Total}\mathrm{Long}-\mathrm{Run}\mathrm{Differential}\equiv {\pi }_{\mathrm{i}}-\pi =-{\gamma }_{\mathrm{i}}+\left(1-{\theta }_{\mathrm{i}}\right)\cdot {\pi }_{\mathrm{i}}\\ ={\delta }_{\mathrm{i}}^{\neg \mathrm{d}}+{\delta }_{\mathrm{i}}^{\mathrm{d}}\cdot {\pi }_{\mathrm{i}}\end{array}$$

where ${\delta }_{\mathrm{i}}^{\neg \mathrm{d}}=-{\gamma }_{\mathrm{i}}\equiv$ non-dynamic differential, and ${\delta }_{\mathrm{i}}^{\mathrm{d}}=\left(1-{\theta }_{\mathrm{i}}\right)\equiv$ dynamic differential. Here, the weight given to the dynamic differential is not the long-run general profit rate, but the i^th industry’s long-run profit rate. Following the same logic as in our previous case, we can proxy this long-run rate with the mean value of the i^th industry’s profit rate series, ${\overline{\pi }}_{\mathrm{i}}$ . The variance of the long-run differential in this case is given by:

(11) $$\mathrm{Var}\left({\widehat{\delta }}_{\mathrm{i}}\right)=\mathrm{Var}\left(\widehat{{\delta }_i^{\neg \mathrm{d}}}\right)+{\overline{\pi }}_{\mathrm{i}}^2\cdot \mathrm{Var}\left(\widehat{{\delta }_i^{\mathrm{d}}}\right)+2\cdot {\overline{\pi }}_{\mathrm{i}}\cdot \mathrm{Cov}\left(\widehat{{\delta }_i^{\neg \mathrm{d}}},\widehat{{\delta }_i^{\mathrm{d}}}\right)$$

Next, in the case where the Bounds Test either finds no long-run relationship between π_{i, t} and π_t or concludes that there exist two long-run relationships between them, and these series are non-stationary, the long-run parameters used to compute the profitability differentials are obtained from the estimation by Fully Modified OLS of the following cointegrating equation:

(12) $${\pi }_{\mathrm{i},\mathrm{t}}={\mathrm{\gamma }}_{\mathrm{i}}+{\theta }_{\mathrm{i}}\cdot {\pi }_{\mathrm{t}}$$

The differentials, which adopt the same form as in Equation (8), can then only be computed in those cases where the Engle and Granger cointegration test identifies a cointegration relationship between the variables. The variance of the long-run differential is given by the expression in Equation (9), with the difference that now there is no need to proxy the covariance between the dynamic and non-dynamic differentials, since it can be directly obtained from the variance-covariance matrix of the cointegration parameters.

Finally, we consider the case where the i^th industry’s profit rate and the general profit rate are both stationary, and the Bounds Test concludes that more than one long-run relationship exists between them. Under such circumstances, which, as discussed in Section 7, are true for all the incremental profit rates, the alternative becomes to compute the profitability differentials by estimating Equation (12) with the use of the Least Squares method, since the stationarity of the variables imply that such regression already represents the long-run relationship between them. In this scenario the differentials are also given by the expression in Equation (8). There is also no need to proxy the covariance between the dynamic and non-dynamic differentials, and the variance of the total differential is given by Equation (9).

The methodology developed in this section, while being more analytically powerful than that of the AR(1) approach, nevertheless has the deficiency of compelling the researcher to omit the results from those industries for which no unique long-run relationship between π_i,t and π_i,t can be found by either the ARDL procedure or any of its alternatives. For this reason, the results from both the AR(1) and ARDL methodologies should be used jointly in the study of profit rate equalisation, since even if there are some industries for which the long-run premia estimated with the latter methodology have to be omitted, the results from the former can still be reported and analysed. Reporting the results from both methodologies also allows the researcher to make a comparative analysis and attain a more robust conclusion.

6. Evidence on Average Rates of Profit

An industry’s average rate of profit is an indicator of the general profitability conditions of all its capitals, rather than just a subset of them, given by the ratio of the total profits earned in the industry to its total stock of capital; that is:

(13) $${\overline{\overline{\mathrm{\pi }}}}_{\mathrm{i},\mathrm{t}}=\frac{{\prod }_{\mathrm{i},\mathrm{t}}}{{\mathrm{{\rm K}}}_{\mathrm{i},\mathrm{t}}}={\mathrm{i}}^{\mathrm{t}\mathrm{h}}\mathrm{Industry},\mathrm{s}\mathrm{Average}\mathrm{Profit}\mathrm{Rate}$$

where Π_i,t  i^th Industry’s Aggregate Profits, and $K_{\mathrm{i},\mathrm{t}}\equiv$  Industry’s Aggregate Capital Stock. The empirical measurement of average profit rates thus requires data on these aggregates at the industry level, which, for the purposes of this study, must be expressed in real terms.

The annual data on the main variables used to conduct such a task for the Norwegian economy was extracted from the OECD’s STAN database, ¹² and the annual CPI data employed to convert the variables that were provided only in nominal terms into real variables was taken from the FRED database. ¹³ The variables of the STAN database whose data was considered are total employment (EMPN); employees (EMPE); labour compensation of employees (LABR); net capital stock (CPNK) and net operating surplus and mixed income (NOPS). The average profit rates were then calculated according to the following formula:

(14) $${\overline{\overline{\pi }}}_{\mathrm{i},\mathrm{t}}=\frac{{\mathrm{NOPS}}_{\mathrm{i},\mathrm{t}}-\left[\frac{{\mathrm{LABR}}_{\mathrm{i},\mathrm{t}}}{{\mathrm{EMPE}}_{\mathrm{i},\mathrm{t}}}\cdot \left({\mathrm{EMPN}}_{\mathrm{i},\mathrm{t}}-{\mathrm{EMPE}}_{\mathrm{i},\mathrm{t}}\right)\right]}{{\mathrm{CPNK}}_{\mathrm{i},\mathrm{t}}}$$

where, for a certain year, the numerator represents the aggregate real net profits earned in the industry accounting for the wage equivalent of the self-employed ¹⁴ (given by the term in brackets), and the numerator contains the aggregate net stock of capital in such industry.

This study counts with data on 26 Norwegian for-profit industries (listed in the appendix, Table A1) over the years 1971–2017. Figure 1 reports all the average profit rates together with their combined mean. Most of these profit rates are considerably clustered around a common level and exhibit numerous crossings, thereby indicating that there could exist a general tendential equalisation between the series. Nonetheless, there appear to be some industries whose average profit rates are persistently above or below the mean, which is made clearer in Figure 2 (see appendix A) where the differences between each profit rate from the mean are reported, making it reasonable to expect from the application of our formal equalisation tests the finding of certain statistically significant positive and negative premia.

Figure 1.

Norwegian Average Rates of Profit, 1971–2017

Figure 2.

Deviations from the Mean, Norwegian Average Rates of Profit, 1971–2017

The formal testing begins with the application of the AR(1) methodology, focused on the profit rate deviation series reported in Figure 2. Following the discussion in Section 4, stationarity tests were first conducted on these series. The results from the non-linear KSS unit root test, reported in Table A2, show that the null hypothesis of the difference series being non-stationary can be directly rejected in 14 industries at the 5% significance level. There were doubts pertaining to the stationarity of the difference series of industries 5, 7, 14, 21, and 23, so the decision was made to complement the KSS results with those of the ADF and the PP tests. The results (not shown here) concluded that these five series were weakly stationary, so the decision was made to employ them in the AR(1) equalisation test without prior detrending. Industries 1, 4, 9, 10, 11, 13, and 20, for which the non-stationarity null hypothesis could not be rejected, were detrended by means of first-order differentiation.

The AR(1) process results, ¹⁵ reported in Table A3, confirm the intuition that there could exist some industries in the sample featuring statistically significant either positive or negative long-run profitability premia, which in this model are given by the α_i. There are 12 industries featuring statistically significant premia, taking the 5% significance level as a reference, and their estimates range from −0.095 (industry 24) to 0.126 (industry 2). Given that even the statistically significant profitability premia are considerably small, the largest of them only reflecting a positive long-run deviation of 12.6 percentage points from the competitive rate and most of these premia being negative and bellow 10 percentage points in absolute value, the results can be said to show the existence of a generalised, albeit weak, tendency for average profit rates to get equalised in the Norwegian economy. Furthermore, the adjustment speed parameters, β_i, are shown to be generally closer to 1 for those industries whose long-run premia are larger in absolute value. This means that the industries with higher differentials tend to see their premia converge in a slower fashion to their long-run value than the industries with smaller differentials.

Turning now to the application of the ARDL approach, the first step taken was, following the discussion in Section 5, to evaluate the stationarity of the average profit rate series by means of the ADF unit root test. The results, reported in Table A4, show that for most of these rates (16 out of 26) the null hypothesis of the existence of a unit root could not be rejected at the 5% significance level. This table reports only the ADF test results of the combined mean of all average profit rates as representative of those of all general rates of profit, since they are very similar to one another, which shows that these rates are also non-stationary. This finding, combined with the aim to include as many industries in the analysis as reasonably possible, thus led to the adoption of the critical value associated with the upper bound’s 10% significance level as the minimum criteria to be met by the F-statistic of the ARDL Bounds Test to reject the null hypothesis of no long-run relationship between π_i,t and π_i. This value, ¹⁶ taking as a reference the case with 45 observations (which are two less than in the sample), is equal to 3.73, so the alternative hypothesis of the Bound Test was accepted only where the test’s F-statistic is larger than such value.

Table A5 reports the results of the ARDL regressions. Insufficient evidence to accept the hypothesis of a long-run relationship between π_i,t and π_t resulted in the omission of the results from industries 1, 2, 16, 17, 20, 22, and 24. Industry 21 was also added to the list of omitted results for exhibiting two long-run relationships between our variables of interest. Nevertheless, since all these industries feature non-stationary averages and general profit rates, they could still be subjected to the Engle and Granger cointegration analysis approach. The results, presented in Table A6, show that a cointegration relationship could only be found for two of those industries (21 and 22) taking the 10% significance level as a minimum requirement, so their long-run differentials could be estimated directly from the estimation of Equation (12) by Fully Modified OLS. ¹⁷ Given how close to the 10% level the relationship for industry 16 is, its results were also included. The remaining industries (1, 2, 17, 20, and 24), however, had to have their results omitted altogether.

Table 1 reports the total, dynamic and non-dynamic long-run differentials estimated for all the 21 industries to which the methodology developed in this study could be applied, together with the long-run profitability premia estimated with the AR(1) methodology. Here, the estimates of the total long-run differentials, δ_i, can be directly compared to those of the long-run premia, α_i. These, even as they are the result of distinct econometric approaches, are remarkably similar and point toward the same conclusion pertaining to the equalisation of average profit rates in the Norwegian economy. As far as the direction of the estimated premia is concerned, we can see that the two approaches differ in only three instances (industries 4, 13, and 15), where they nevertheless agree on the fact that they are not statistically significant. Concerning the magnitude and statistical significance of the premia, at the 5% significance level the methods produce different results in four cases (industries 6, 12, 22, and 25), but out of these only three were left at the 10% significance level (industries 12, 22, and 25). Given how similar the results produced by both methods are, the union of the two sets of industries featuring statistically significant profitability premia is concluded to represent those industries whose average profit rates do not converge toward the competitive rate; that is, the conclusion is that there are 12 industries in the Norwegian economy that are earning average profit rates either above or below the competitive rate, since at least one of the two methods detected that their long-run profitability premia is statistically significant.

Table 1.

Long-Run Differential Cross-Method Comparison, Average Profit Rates

Note: T-ratios are reported in parenthesis.

Regarding the dynamic and non-dynamic differentials, the results strongly favour the interpretation advanced in Section 5, since they show that, for most industries, these have opposite signs and are inversely proportional in magnitude, thereby indicating that they tend to cancel each other out, which gives a highly valuable insight into the factors leading to the majority of total differentials being statistically insignificant and small in absolute vale. In short, what these results show that could not be identified with the AR(1) method is that there is a general tendency for the industry-specific average profit rates to adjust to the general profitability conditions in such a manner that the part of their premia due mainly to idiosyncratic factors does not translate into significantly large total long-run premia.

Overall, the evidence on Norwegian average profit rates therefore shows a general but weak tendential equalisation, and as such matches the hypothesis on average profitability differentials drawn from the Theory of Real Competition discussed in Section 3.

7. Evidence on Incremental Rates of Return

Thus far the empirical analysis has been centred around the inter-industry average profit rates, which, under the Theory of Real Competition, are not expected to exhibit a strong equalisation tendency due to the existence of a systematic dispersion of the profit rates earned across each industry’s capitals, whereby some of such capitals represent older, less accessible methods of production unlikely to be the target of competitive investments flows. In a competitive market economy, the newer investments target the best generally reproducible production conditions in the industry embodied by its regulating capital, and it is the returns earned on such capitals across industries that are expected to get equalised in the long run. In the short run, however, the turbulent nature of for-profit competition is expected to give rise to remarkably volatile regulating profit rates, with some industries earning exceptionally high or low short-run premia.

An industry’s regulating rate of profit can be approximated by the profit rate earned on its newly formed capital, since it is this capital that best approximates the regulating conditions of production in the industry. Such profit rate, which in the literature is known as the incremental rate of return, was first analytically derived by Shaikh (1997), and is given by the ratio of the change in profits to the previous year’s investment; that is, for the i^th industry:

(15) $${\tilde{\mathrm{\pi }}}_{\mathrm{i},\mathrm{t}}=\frac{\mathrm{\Delta }{\prod }_{\mathrm{i},\mathrm{t}}}{{\mathrm{I}}_{\mathrm{i},\mathrm{t}-1}}=\mathrm{Incremental}\mathrm{Profit}\mathrm{Rate}\approx \mathrm{Regulating}\mathrm{Profit}\mathrm{Rate}$$

where ${\mathrm{I}}_{\mathrm{i},\mathrm{t}-1}\equiv {\mathrm{i}}^{\mathrm{th}}$ industry’s previous year’s investment (capital formation).

The empirical measurement of the incremental rates of return in the Norwegian economy made use of the same databases as in the previous section. The STAN database’s variables considered in this case are total employment (EMPN); employees (EMPE); labour compensation of employees (LABR); gross fixed capital formation (GFCF) and gross operating surplus and mixed income (GOPS). The same FRED data on CPI was also used to convert nominal variables into real ones. The real ¹⁸ incremental rates were then computed according to the following formula:

(16) $${\tilde{\mathrm{\pi }}}_{\mathrm{i},\mathrm{t}}=\frac{\mathrm{\Delta }\left[{\mathrm{GOPS}}_{\mathrm{i},\mathrm{t}}-\left[\frac{{\mathrm{LABR}}_{\mathrm{i},\mathrm{t}}}{{\mathrm{EMPE}}_{\mathrm{i},\mathrm{t}}}\cdot \left({\mathrm{EMPN}}_{\mathrm{i},\mathrm{t}}-{\mathrm{EMPE}}_{\mathrm{i},\mathrm{t}}\right)\right]\right]}{{\mathrm{GFCF}}_{\mathrm{i},\mathrm{t}-1}}$$

where the numerator expresses the change in real gross profits at a given year, and the denominator represents the previous year’s real gross investment.

Figure 3 presents the incremental profit rates of all 26 Norwegian industries listed in Table A1. These, as expected, are considerably more volatile than their average counterparts. They are also more clustered together and exhibit a larger number of crossings, indicating that their propensity to get equalised in the long run is likely stronger. The same conclusion can be obtained from a visual inspection of the deviation series reported in Figure 5, since these cross multiple times the zero-line and do not appear to diverge significantly from it. Notably, the incremental profit rates and their deviations are trivially stationary according to all unit root tests (results not shown here).

Figure 3.

Norwegian Incremental Rates of Profit, 1971–2017

Furthermore, Figure 4 presents the economy-wide incremental rate of profit together with its average counterpart, showing a joint behaviour that closely resembles the postulates of the Theory of Real Competition: the incremental rate of profit, while being more volatile (due to the turbulent nature of capitalist accumulation), gravitates around the average and moves in the same direction, sharing with it a similar long-run mean. Thus, the main difference between the series is their volatility, which is in turn explained by the fact that the incremental rate of profit embodies the profitability conditions of the economy’s regulating capitals, which are subject to the chaotic behaviour of short-run investment inflows and outflows.

Figure 4.

Norwegian Economy-Wide Incremental and Average Rates of Profit, 1971–2017

The stationarity of the incremental profit rates and their deviation series had two consequences: firstly, there was no need to detrend any of the deviation series before the estimation of the AR(1) model. Secondly, since the ARDL Bounds Test found two long-run relationships between the industry-specific incremental rate of return and the general profit rate for all industries in the sample (results not shown here), the simpler alternative discussed in Section 5 of obtaining the total, dynamic and non-dynamic differentials from the estimation of Equation (12) by the Least Squares method was undertaken, and there were thus no industries whose results had to be omitted as in the case of the average rates of profit.

The results from the AR(1) and the static regressions ¹⁹ are reported, respectively, in Tables A7 and A8. Table 2 presents the long-run premia obtained with the first method together with the long-run differentials of the second, showing that the total long-run premia estimated by the two methods are even closer to one another than in the case of average profit rates. As far as the sign and magnitude of the total premia are concerned, these methods produce nearly identical results. They only differ in the significance of the premia earned by three industries (6, 23, and 24) at the 5% significance level, reduced to just one at the 10% level (industry 24).

Table 2.

Long-Run Differential Cross-Method Comparison, Incremental Profit Rates

Note: T-ratios are reported in parenthesis.

In this case, the union of the two sets (corresponding to the two methodologies) of industries featuring statistically significant premia thus includes industries 6, 23, and 24. According to both approaches, the highest of these premia, that of industry 23, is in the vicinity of 30 percentage points, which more than doubles the highest statistically significant premium identified in the average profit rates case. The premia of industries 6 and 24, whose average profitability differentials were also statistically significant, are negative and not nearly as large in absolute value as the premium of industry 23. Therefore, whereas the results overwhelmingly point toward a strong equalising tendency for Norwegian regulating profit rates, there is a clear outlier earning remarkably higher returns. Such an outlier, the financial and insurance activities industry, is characterised by a high market share concentration ²⁰ that could be the source of significant barriers to entry not allowing for a competitive adjustment of its returns toward the economy-wide norm. This conclusion is supported by the industry’s dynamic and non-dynamic differentials, which show how the idiosyncratic factors affecting its profitability (among which persistent barriers to entry are included) imply a positive premium of 38.5 percentage points that is not sufficiently counteracted by the dynamic adjustment of its regulating profit rate toward the general rate. The dynamic differential is thus not small enough for the industry’s regulating profit rate to match the general rate.

Therefore, despite the outlier, Norwegian incremental rates of return show a strong long-run equalisation tendency. The dynamic and non-dynamic components of the total differentials tend to cancel each other out as predicted by our theory, thereby yielding statistically insignificant premia for 23 out of the 26 industries in the sample.

Figure 5.

Deviations from the Mean, Norwegian Incremental Rates of Profit, 1971–2017

8. Summary and Conclusion

This study provides a theoretical and empirical inquiry into the question of the tendential equalisation of profit rates across economic sectors as it relates to broader theories on competition. The theoretical framework adopted to this end is that of the Theory of Real Competition, which was contrasted to contending theories that approach the question by conceiving of competition as an equilibrium state representing an ideal scenario and attempting to explain the real economic phenomena either by sticking to such notion or by describing the world as an imperfect version of it. In direct opposition to such approaches, the Theory of Real Competition conceptualises competition as a process characterised by a war-like struggle where investment decisions in response to profitability differentials do not follow an orderly path, but rather a turbulent and chaotic one from which a long-run order can nevertheless be derived. Key to this theory is the distinction between an industry’s average and regulating profitability conditions. Given the natural dispersion of profit rates within industries in light of equal selling prices across an industry’s firms but unequal cost structures among its capitals, the theory predicts that average profit rates in competitive economies will exhibit either a weak long-run tendential equalisation or no such tendency altogether. However, regulating rates of profit, which are directly targeted by the newest for-profit formation of capital, are expected to feature a much stronger equalising tendency.

The econometric approaches to the empirical examination of profit rate equalisation employed consist of an AR(1) methodology commonly used across the literature and a novel methodology first systematised in this study, centred around the ARDL approach to cointegration analysis, but also extended to account for specific cases where the ARDL modelling cannot be applied. The new methodology has the advantage of yielding an estimate of each industry’s total long-run profitability premium while allowing the researcher to distinguish between the part of such premium due to factors idiosyncratic to the industry, and that related to the manner in which its profit rate adjusts to the general profitability conditions in the economy. Nevertheless, it has the disadvantage of being applicable only where a long-run relationship between an industry’s profit rate and the combined profit rate of all other industries can be established.

Empirical equalisation tests were conducted on Norwegian average and incremental profit rates, covering the years 1971–2017. The results show, on the one hand, that 12 out of the 26 industries in the sample exhibit statistically significant average profitability differentials, but that these are mostly negative and, only in one instance, larger than 10 percentage points in absolute value. On the other hand, the evidence on incremental profit rates shows that just three industries have statistically significant regulating profitability differentials, and only one of them features a large, positive premium that could reflect the existence of barriers to entry inhibiting the adjustment of its profit rate toward the competitive norm. Notably, the results from the dynamic and non-dynamic components of the total differential evidence that these tend to counteract each other for both average and incremental profit rates, which explains the small total differentials present in most industries. Overall, the findings from the Norwegian economy are thus in line with the hypotheses drawn from the Theory of Real Competition.

Appendices

Appendix A. List of Industries and Tables for Sections 6 and 7

Table A1.

List of 26 Norwegian Industries

Table A2.

Non-linear KSS Unit Root Test Result, 26 Average Profit Rate Deviation Series

Note: The Akaike Information Criteria (AIC) was employed as the lag order selection criteria for the number of lags of the dependent variable in the test’s re-parametrised equation. The symbols *, **, and *** denote, respectively, rejection of the null hypothesis (existence of a unit root) at the 0.10, 0.05, and 0.01 significance levels. The symbols t_KSS1 , t_KSS2 and t_KSS3 represent the test’s t-statistic on the raw, demeaned, and detrended data, respectively. The critical values were retrieved from Kapetanios, Shin, and Snell (2003).

Table A3.

AR(1) Results, 26 Norwegian Average Profit Rate Deviations from the Mean

Note: T-ratios are reported in parenthesis. The industries marked with an asterisk have been detrended prior to the estimation of the AR(1) process.

Table A4.

Augmented Dickey–Fuller Results, 26 Average Profit Rates and Their Mean

Note: P-values are reported in parenthesis. The symbol t_ADF1 represents the t-statistic of the ADF test on the data with a constant and trend. The symbols t_ADF2 and t_ADF3 represent, respectively, such statistics for the data with a trend only and the data without a constant or a trend. The symbols *, **, and *** denote, respectively, rejection of the null hypothesis (existence of a unit root) at the 0.10, 0.05, and 0.01 significance levels. The one-sided p-values are retrieved from MacKinnon (1996).

Table A5.

ARDL(p,q) Results, 26 Norwegian Average Profit Rates

Note: T-ratios are reported in parenthesis. Each model’s number of lags was selected in accordance with the Akaike Information Criteria. The symbol F(π_i|π) represents the F-statistic of the Bounds Test when the general rate of profit is the independent variable, and F(π|π_i) represents such statistic when it is the dependent variable. The symbols *, **, and *** denote, respectively, rejection of the null hypothesis (no long-run relationship) at the 0.10, 0.05, and 0.01 significance levels. All critical values are retrieved from Narayan (2005).

Table A6.

Fully Modified OLS Results, Non-stationary Average Profit Rates

Table A7.

AR(1) Results, 26 Norwegian Incremental Profit Rate Deviations from the Mean

Table A8.

Static Regression Results, 26 Norwegian Incremental Profit Rates

Notes

1.

See, as examples, Bain (1951) and Stigler (1963). Weiss (1974) provides a comprehensive list of these studies. Semmler (1984) critically examines the main works of this first generation.

2.

See Mueller (1977, 1986, 1990) and Geroski (1990).

3.

The concept, inspired by the Elton and Gruber (1991) financial economics textbook, had been earlier used in an empirical work on stock prices (Shaikh 1997).

4.

A detailed explanation of the entire procedure and interpretation can be found in Section 5.

5.

See Mankiw (2016), Varian (1993), and Jehle and Reny (2011) for an introductory, intermediate, and advanced, respectively, account of perfect competition.

6.

In some instances, we may even find firms that, in their cutting of prices, willingly incur temporary losses with the aim of consolidating a bigger market share.

7.

Evidence from the US (Kaplan and Menzio 2014) favours such analysis.

8.

The only instance where the average profitability conditions are the regulating ones would then be in an industry where the average production conditions are exactly the best generally reproducible ones, something that is considerably unlikely.

9.

This procedure applies equally to average and incremental profit rates.

10.

See Kapetanios, Shin, and Snell (2003).

11.

While equivalent in notation to the mean of all profit rates employed in the previous section, the general rate of profit in this section differs from it by not including the i^th industry’s profit rate, and thus by varying from industry to industry, although the differences are small for samples that include many industries (as is the case here), since only one industry is removed from each successive computation of the general rate of profit.

12.

The STAN database can be accessed at https://www.oecd.org/industry/ind/stanstructuralanalysisdatabase.htm.

13.

The FRED database can be accessed at https://fred.stlouisfed.org/.

14.

Such correction allows for a more precise calculation of industry profits, following Duménil and Lévy (2002) and Shaikh (2008, 2016).

15.

Residual autocorrelation and heteroskedasticity tests were conducted on each of the 26 regressions. HAC (Newey–West) standard errors and covariances were used in those regressions featuring any of these phenomena, which were detected for industries 5, 8, 10, and 26.

16.

Retrieved from Narayan (2005).

17.

Residual heteroskedasticity tests were conducted on the ARDL and cointegration regressions. It was detected on the ARDL regressions for industries 13 and 15 and corrected with HAC (Newey–West) standard errors.

18.

Both the incremental and average rates of profit are in real terms to allow for a direct comparison between them. Whereas it could have been possible to include the incremental rates in current prices, due to a lack of data on the nominal net capital stock, this could not have been done in the case of the average rates. However, both the real and nominal incremental rates of profit exhibit very similar behaviours, so it is expected that the results obtained in this article would closely resemble those that could be obtained under an analysis of the nominal incremental and average rates of return.

19.

All the regressions with incremental profit rates were also subjected to residual autocorrelation and heteroskedasticity tests. HAC (Newey–West) standard errors and covariances were once again used in the regressions exhibiting any of these phenomena.

20.

See Norges Bank (2021) and Sampo Group (2022).

References

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