Capital in Netherlands
19212013 & Piketty’s formula
Summary
Summary of
article in ESB Jaargang 100 (4704) 26 February 2015,
by Dr. Marein van Schaaijk
Click
here to download Kapitaal NLD.xls with the
underlying data
FORMULA
Piketty
(2014) presents in his splendid book for several countries for several
periods
a treasury of data concerning the private rate of return on capital, r,
the
rate of growth of income and output, g and the capital/income ratio,
K/Y. Based
on his empirical analysis using graphs, he finds his third formula: The
Central
Contradiction of Capitalism: r > g. His conclusion is:
“The principal destabilizing force
has to do with the fact that the private rate of return on capital, r,
can
be significantly higher for long periods of time
than the rate of growth
of income and output, g. The inequality r
> g implies
that wealth accumulated in the past grows more rapidly than output and
wages.”
However, ”significantly higher for
long periods of time” what
does that
exactly mean? So first we try to find out what is exactly the relation
between,
r, g and K/Y.
In sheet
Formulas in Van Schaaijk,
2015, you can find that there exists a definition relation:
p*r –g = z
in which p = dK/W (the investment
ratio / profit rate), and z the percentage growth rate of K/Y
Given this definition follows: If r
> g/p then z > 0
However
Piketty’s conclusion “The
inequality r > g implies
that wealth accumulated in the past
grows more rapidly than output and wages”, is only true for
certain values of
p.
So if
you change in the third
formula of Piketty ”significantly higher for long periods of
time” into
“1/p” then Piketty’s third formula
becomes a definition equation, and that is true always and everywhere.
So not
only this century but also next and not only in the countries that
Piketty
studied but all countries. So
no
empirical work needs to be done to come to this conclusion for example
for the Netherlands
during 1921 – 2013.
Actually, also concerning the
second
formula of Piketty a definition equation can be derived, see in sheet
Afleiding
formules in Kapitaal NLD.xls.
Capital
in Netherlands 19212013
A lot
of methodological problems are
there when calculating longer time series for capital. See Coenen, ESB,
2622015. We made several time
series, see KapitaalNLD.xls
on www.micromacroconsultants.com
In the
graph below we present two of
them for the Netherlands
for the period 19212013. One V1/Y NLD, based on wealth statistics, and
the
other one K1/Y NLD based on cumulated net real investments with
starting point taken in 1947 from the figure of the wealth statistic.
Furthermore in the graph below
we
show the K/Y for the World 18702100
from Piketty’s graph 12.4
Source: Piketty, 2014 Graph
12.4 and van Schaaijk,
KapitaalNLD.wks January 2015
The
graph shows big differences
between K1/K NLD and V1/Y NLD, but in both cases there was a big
decrease
between 1921 and the seventies (in Netherlands much more then in the
World), then
a slight increase, followed by stabilisation of the last thirty years
in case of K1/Y,
but some increase in V1/Y. In the World the last thirty years show an
increase, and
Piketty expects a further increase.
Conclusions
In
this article is shown that
Piketty’s third formula could be made more precisely by
bringing in it a factor
p (the ratio of investment/profits). Then a definition equation
results. Such
equations do not need to be proved by empirical analysis. So instead of analyzing r
and g one can
immediately start analysing K/Y. That
is
what has been done for Netherlands.
Is the decrease of K/Y between 1921
and the seventies the result of capital saving technical progress or
changes in
wage costs per product? It
might be
interesting to analyse Dutch capital stock data that are available per
sector
of industry.
Answering those questions is beyond
the scope of this brief article.
Literature:
 Piketty, T., Capital
in
twentyfirst century, The Belknap Press of Harvard
University Press.
Cambridge, Massachusetts, London, England,
2014
 Van Schaaijk, M. van (2015) KapitaalNLD.xls (in
Dutch) on www.micromacroconsultants.com
 Schaaijk,M. van (2015) Kapitaal in Nederland,
ESB Jaargang 100 (4704) 26 February 2015
Addendum
2nd March 2015
We mentioned already that also concerning the
second formula of Piketty a definition equation can be derived. What does this
mean?
We know:
z = k – g The percentage growth
rate of K/Y z, is the percentage growth rate of capital k, minus the percentage
growth rate of Y, g. And savings rate s
= S/Y*100.
k = dK/K *100
= (dK/S)*(S/K) *100 =
(dK/S)*(S/Y)*(Y/K) *100
so k = (dK/S)*s/(K/Y)
so z = (dK/S)*s/(K/Y)  g
so
if z = 0 and dK=S then
K/Y
= s/g This is Piketty’s second formula
Please
note that K/Y = s/g is only true if z =
0 and dK = S It is a little bit
strange to use this formula that assumes K/Y to be stable, to forecast changes
in K/Y.
Piketty
assumes that world g will decrease from more then 3 now to below 1,5 and that s
will stabilise around 10 percent. If in the formula K/Y = s/g you divide g by 2, then K/Y will become twice
as big. And that is what Piketty shows in his graph 5.8. His main conclusion
and fear is that K/Y will increase a lot this century, and might even go up to
the level of the beginning of last century.
However
assume for example g becomes 0, then, following Piketty’s formula, K/Y becomes
infinitive (!?) and should g change from 3 to – 3 then K/Y does not change in
number, but becomes negative (!?)
So
it looks like that Piketty’s second formula cannot be used to forecast K/Y.
Piketty
wrote a beautiful book with a lot of interesting information, only he might
reconsider to revise his second and third formula. That could also result in
another conclusion concerning K/Y growth during this century.
He
might just use z = k – g if he wants to
forecast the effect of X lower increase in g (because of lower population
growth) on z. All other things equal (like k)
X lower g means X higher z.
But K and g are not independent of each other.
If g goes down businesses need less growth of machinery and buildings, so
sooner or later you might expect also k to go down. In case savings at the same
time go up (because maybe expected ageing of population in the future one might
save more now). Thanks to deficits on the capital account of the Balance of
Payments, the national Wealth/ Y ratio might increase even when domestic K/Y is
stable.
