What if Factor Shares are not Constant? Implications for
Growth and Business Cycle Theories.
by
Michele Boldrin (University of Minnesota)
Carmen Garrido Ruiz (Universidad Carlos III, Madrid)
Standard business cycle theories, either of the real or imaginary type, share few things in
common. Constancy of the shares of national income going to labor and capital
respectively is one of them. The same is true for many different theories of economic
growth, be them of the exogenous, endogenous, or undecided type: almost all of them
assume constancy of the income shares of labor and capital. There are few exceptions to
this rule, which we examine in due course. Basic theoretical models of growth and/or
business cycles are, in turn, the workhorses in almost all applied fields of modern
macroeconomics, from public finance, to labor economics, to asset pricing. One is
therefore legitimate to ask: what is the empirical evidence supporting this widely-held
hypothesis?
Cursory and also not-so-cursory reading of the macroeconomic literature suggests that
the origin of the constancy hypothesis is Lord Kaldor’s famous six stylized facts of
economic growth, together with analytical convenience. Kaldor’s stylized “facts” are not
exactly based on what one would call “careful” empirical work and very few of them (if
any) appear to correspond to statistical facts either at the time of his writings or later on.
Curiously enough, while those facts are clearly contradicted by most of what we know
about growth, i.e. balanced growth at a constant rate is NOT the way economies grow,
capital/output and factors ratios in general are NOT constant, the rate of return on capital
is NOT constant, technological progress does NOT take place at some constant rate (ever
heard of the productivity slowdown?), economic theorists and practitioners alike seem to
keep building models in which those hypotheses hold. Arguably, the constancy of factor
shares is the key belief holding all these “facts” together. Hence the need and value of reconsidering the empirical foundations of the constancy of factor shares hypothesis.
In this paper we begin doing this by looking at both Spanish and USA data since the
1950s. Our procedure is the following. First we try defining what “constant” and “not
constant” factor shares may possibly mean. Obviously, a monotone trend in either of the
shares is out of question, as it implies that all national income accrues eventually to one
of the factors of production. Concentrate on the share of labor in national income from
now on, to simplify exposition. This can only fluctuate within a certain band, which
immediately leads to the temptation of taking long run averages and claiming that it is
constant. This is what most economists usually do, attributing the oscillations around the
long-run average as due to some irrelevant and unexplainable randomness. Hence, to
argue that the lanor share is not constant one must, at least, do the following three things:
-
argue that the band within which the labor share fluctuates is “too large” to be the
result of some random additions to an underlying constant value;
argue that the upward and downward swings are both ample enough and long
enough to be inconsistent with the “random addition” hypothesis;
show that the upward and downward movements are “systematic”, i.e. that they
have a statistical structure which is not reducible to white noise and that they can
be persuasively associated to contemporaneous movements of other, relevant,
socio-economic variables.
This is what we try to accomplish. We begin with the aggregate Spanish time series, and
address a continuously debated measurement issue, i.e. how should “mixed income” be
allocated between capital and labor? We argue this is a decoy: no matter which is adopted
of the three or four ways in which mixed income can reasonably be split between capital
and labor, the resulting movements in labor share are the same; only the level changes
systematically. Next we show that the share of labor in national income changes
dramatically in Spain, and that the band of oscillation is very large: more than 10
percentage points. Second we show that the upward and downward swings have enough
persistence and statistical structure to reject any randomness hypothesis. Before moving
to stage three, i.e. asking if there is some economic meaning in the observed oscillations,
we look at disaggregated data. More precisely, we use the FBBVA and the MORES data
sets to study the behavior of the labor share at the regional and sectorial levels. The
“regional’ breakdown is that of the 17 Spanish Autonomias, while the “sectorial” one is
in 15 private sectors plus the residential and the public sectors. We show that the
movements observed at the aggregate level persist at the regional/sectorial levels and
that, when they do not (as it is the case mostly with the agricultural sector) a very clear
and immediate explanation is available in terms of “structural change”. Movements in the
regional shares of labor, in particular, are neatly decomposable into a “sectorial
composition” effect and an “aggregate effect”. The first refers to the fact that sectorial
labor shares are systematically and persistently very different across sectors (the range
being of the order of 50 percentage points of sectorial value added!); the second refers to
the fact that very common long-run trends are visible in the sectorial labor shares which
are parallel to the national ones. This allows us to go back to the aggregate labor share
and separate the “sectorial composition effect” from the total. Both are statistically very
relevant, and in both the cases the “randomness” hypothesis is easily rejected.
At this point the following hypothesis is advanced: movements in (aggregate) labor share
are the composition of two determinants: structural change, consisting of (i) the decrease
of the share of agriculture, (ii) the steady increase in the share of services, and (iii) the
increase-then-decrease in the share of industry; cyclical or social conflict, the meaning of
which we will discuss shortly.
We move next to the US data, and apply the same procedure. Regional data are not
available here, but sectorial data are. We show the following: while of much smaller
amplitude (about 5 percentage points of national income) fluctuations in the share of
labor are persistent also here, both at the aggregate and sectorial levels; differences in the
sectorial levels of the labor share are very large and highly persistent, roughly of the same
order of magnitude as in Spain; sectorial movements in the labor share are highly
correlated with movements in the aggregate share. Remarkably enough, as in the
aggregate Spanish data once the structural change component has been eliminated, the
share of labor in national income is highly countercyclical. The structural change
component, we show, is much smaller in the US data, mostly because the decrease in the
share of agriculture was almost completed when our time series start, 1958.
Next we try to assess, empirically, if the variability of factor shares, at the national and
sectorial level, are compatible with a CES production function with a constant elasticity
of substitution other than one. We conclude that, with a few weak exceptions, this is not
the case. So, while sectorial and aggregate production functions with exogenously timevarying coefficients are a way out of the conundrum, we lean toward rejecting them as
“economic engineering”; with due apologies to true engineers, the “engineering” is meant
to be a negative feature here. We next look at other, selected Spanish evidence. We show
that when the labor share grows, this is due to the real wage growing faster than labor
productivity and the capital/labor ratio remaining roughly constant. We also show that,
eventually, the capital/labor ratio does change (it increases), and this is followed by an
increase in labor productivity larger than the increase in the real wage. This brings about,
eventually, a reduction in the labor share of income. Finally, we also show that periods of
high labor productivity growth tend to be associated with periods of high growth, and
tend to follow increases in the capital/labor ratios. This characterization holds, for
Spanish data, both at the aggregate and sectorial level. We are in the process of carrying
out the same analysis for the US aggregate and sectorial data.
Finally, we ask: which model of growth and business cycle is compatible with the
reported facts? While, at this stage, we do not have a fully fledged model to propose, the
following features seem to characterize it:
-
-
technologies are putty-clay;
short-run substitutability between labor and capital is very low, close to zero;
technological progress is factor saving and, in fact, mostly labor saving;
the extent to which factor saving technological changes can be adopted differs
vastly from sector to sector;
the real wage is not determined by the marginal productivity of labor, but by some
form of bargaining (either collective or decentralizeed) between workers and
firms;
capital maximizes profits either by adopting factor saving innovations or by
moving from one firm (sector) to another;
technological innovations and sectorial movements (of capital) are discrete, which
means that an indivisibility/fixed cost is involved; hence capital movements and
technological progress tend to follow threshold rules. This tends to give rise to
endogenous oscillations.