Abstract

The law of the tendential fall in the rate of prot has been at the center of theoretical and empirical debates within Marxian political economy ever since the publication of Volume III of Capital. An important limitation of this literature is the absence of a comprehensive econometric analysis of the behaviour of the rate of prot. In this paper, we attempt to ll this lacuna in two ways. First, we investigate the time series properties of the prot rate series. The evidence suggests that the rate of prot behaves like a random walk and exhibits \long waves» interestingly correlated with major epochs of U.S. economic history. In the second part, we test Marx’s law of the tendential fall in the rate of prot with a novel econometric model that explicitly accounts for the counter-tendencies. We nd evidence of a long-run downward trend in the general prot rate for the US economy for the period 1948-2007.

Keywords: falling rate of prot, Marxian political economy, time series analysis, unit roots.

1 Introduction

Marx’s claim in Volume III of Capital that there is a tendency for the general rate of prot
to fall with the development of capitalism has spawned an enormous and growing literature

often marked by bitter controversy and fruitful debate (Dobb, 1939; Sweezy, 1942, Gilman,
1957; Okishio, 1961; Shaikh, 1978; Wol, 1979; Mandel, 1980; Roemer, 1981; Bowles, 1985;
Foley, 1986; Michl, 1988; Shaikh, 1992; Dumenil and Levy 1993, 1995; Foley and Michl,
1999; Wol, 2001; Dumenil and Levy, 2002a, 2002b; Wol, 2003; Kliman, 2009).1
The theoretical strand of this literature has focused on understanding the possible causes
behind what Marx referred to as the law of the tendential fall in the rate of prot (LTFRP).2
Recall that the rate of prot, in Marx (1993), is dened as

r = s /c + v = (s=v) / 1 + (c=v) = ek;

where r is the rate of prot, s the surplus value, v, the variable capital, c, the constant
capital, e = s=v the intensity of exploitation (also referred to as the rate of surplus value)
and k = 1=(1+(c=v)) the composition of capital (Foley, 1986). The early debate was focused
on two crucial issues. The rst issue pertains to whether the composition of capital falls with
the development of capitalism, i.e., whether the increasing technical composition of capital
translated into an increase in the value composition of capital. The second issue is whether
the increase in the intensity of exploitation is swamped by the fall in the composition of
capital, thereby leading to a fall in the rate of prot (Moseley, 1991).3 A third issue relating
to choice of technique was added to this long-standing debate by Okishio’s (1961) claim to
have disproved the LTFRP. The subsequent theoretical literature can be fruitfully classied
with reference to Okishio (1961), to our mind, into the following three strands.4 The rst
strand accepts the validity of the so-called Okishio Theorem, which is understood as having proved» that the LTFRP can never emerge as a signicant tendency in a capitalist economy
with prot-maximising entrepreneurs and viable technical change; prominent scholars in
this strand include Romer (1981), Bowles (1985) and others. The second strand rejects
the validity of the so-called Okishio Theorem in toto and instead believes that there is a
secular tendency for the rate of prot to fall with capitalist development; prominent scholars
in this strand are Shaikh (1978, 1987, 1992), Kliman (2007, 2009) and others. The third
strand conditionally accepts the validity of the so-called Okishio Theorem, arguing that
the key assumption that drives its result – xed real wages – does not characterise the
actual evolution of capitalism. Thus, neither a secular tendency for the prot rate to fall
nor a secular tendency to increase can be a priori associated with capitalist development;
prominent scholars in this strand are Foley (1986), Michl (1988), Moseley (1991), Dumenil
and Levy (1993, 1995), Foley and Michl (1999), Dumenil and Levy (2003).5

Instead of engaging with this rich theoretical debate in any detail, in this paper our
focus will be towards addressing a dierent but related question: what does the evidence
show regarding the tendency of the general rate of prot to fall in the U.S.? The empirical
strand of this vibrant literature has addressed this issue but without displaying the depth
and sophistication of the theoretical literature. A major lacuna has been the dearth of
serious econometric inquiry to inform an empirical analysis.6 A preponderance of empirical
studies utilize only exploratory techniques (e.g., visual inspection of time series plots) in
order to infer trends in the rate of prot (Gilman 1957; Wol 1979, 2001, 2003; Dumenil and
Levy 1993, 1995, 2002a, 2002b). While visual and exploratory techniques can be valuable
starting points of empirical research, it is necessary to apply modern econometric methods
for investigating trends in the rate of prot (e.g., an investigation of the time-series properties
of the general rate of prot). It is this lacuna in the empirical literature on the LTFRP that we wish to addres.

The analysis in this paper proceeds in two steps. First, we conduct out detailed and
systematic investigation of the time series properties of the general rate of prot in the U.S.
economy using the Box-Jenkins approach to time-series analysis (Box and Jenkins, 1970)
and complementing that approach with a battery of unit root tests. The results of this
analysis suggests that the U.S. rate of prot is a random walk and exhibits \long waves» like
any time series with stochastic trends, conrming the intuitive claims of Mandel (1980) and
Shaikh (1992). Thus, our analysis imparts statistical substance to the long-standing claim
about long waves in the prot rate series.

Using results about the non-stationarity of the prot rate, we proceed in the second part
to econometrically test the LTFRP. We do so by estimating a novel time series regression
model derived from Marx’s analysis in Volume III of Capital. The novelty of our analysis
derives from two aspects of our empirical approach. First, we control for the eects of what
Marx had called \counter-tendencies». Second, we explicitly take account of non-stationary
random variables in our statistical inference. To the best of our knowledge, both these
aspects have not been adequately addressed in the existing literature.

Is there a tendency for the rate of profit to fall? Econometric evidence for the U.S. economy, 1948-2007

Working Paper 2010-04