The document discusses Paul Samuelson and Paul Davidson's views on ergodicity in economics. It summarizes that in 1968, Samuelson wrote that for economics to be a hard science, it must believe in a unique long-run equilibrium independent of initial conditions, which he termed the "ergodic hypothesis." Davidson indicated that Samuelson saw accepting the ergodic hypothesis as necessary for the scientific method in economics. The document also explores debates around determinism, uncertainty, and the use of the term "ergodic" in economics.

1. ©
2014
Dirk
Ehnts
12th International Post-Keynesian Conference (UMKC)
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Dirk
Ehnts,
Free
University
Berlin
Miguel
Carrión
Álvarez,
Banco
Santander
Madrid

2. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Finally, there was an even more interesting third
assumption implicit and explicit in the classical
mind. It was a belief in unique long-run
equilibrium independent of initial conditions. I
shall call it the “ergodic hypothesis” by analogy
to the use of this term in statistical mechanics.
Paul Samuelson, 1969
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
2

3. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Finally, there was an even more interesting third
assumption implicit and explicit in the classical
mind. It was a belief in unique long-run
equilibrium independent of initial conditions. I
shall call it the “ergodic hypothesis” by analogy
to the use of this term in statistical mechanics.
Paul Samuelson, 1969
Furthermore in an article published in 1969
Samuelson argued that the „ergodic hypothesis
[axiom]“ is a necessary foundation if economics
is a hard science [Samuelson, 1969, p. 184].
Paul Davidson, 2006
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
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4. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Ergodicity
in
a
nutshell:
If
you
throw
six
dice
at
one
point
in
>me
and
the
average
is
the
same
as
throwing
a
die
six
>mes
in
a
row,
then
the
ensemble
average
and
the
'me
average
are
iden>cal
–
the
system
is
ergodic.
In
[non-­‐]ergodic
system,
you
can[not]
derive
the
probabili>es
of
a
single
future
event
just
by
looking
at
the
past
historical
development
of
a
single
instance
of
the
system.
14.
April
2014
Neuere
Ansätze
der
Geldtheorie
4

5. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
„by
analogy
to
the
use
of
this
term
in
sta>s>cal
mechanics“:
Hence,
to
the
mythical
ques>on
of
whether
the
ergodic
hypothesis
jus>fies
sta>s>cal
mechanics,
the
answer
is
worse
than
no:
it
is
not
the
right
ques>on.
Indeed,
the
ques>on
cannot
be
anymore
whether
nature
strictly
obeys
the
demands
of
ergodicity;
rather,
the
ques>on
ought
to
ask
how
good
an
idealiza>on
the
theory
really
is.
Emch
and
Liu
(2001,
§9.5)
14.
April
2014
Neuere
Ansätze
der
Geldtheorie
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6. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Economics:
ergodicity
as
shibboleth?
hfp://www.merriam-­‐webster.com/dic>onary/shibboleth
14.
April
2014
Neuere
Ansätze
der
Geldtheorie
6

7. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
“[I]t is possible, but not
necessarily assumed, that an
ergodic state for P [the
probability distribution] will
emerge in the limit as T [time]
goes to infinity.”
Samuelson (1965, 43)
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
7

8. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
“Finally, there was an even more interesting third
assumption implicit and explicit in the classical
mind. It was a belief in unique long-run equilibrium
independent of initial conditions. I shall call it the
“ergodic hypothesis” by analogy to the use of this
term in statistical mechanics. Remember that the
classical economists were fatalists (a synonym for
“believers in equilibrium”!) . Harriet Martineau, who
made fairy tales out of economics (…), believed that if
the state redivided income each morning, by night the
rich would again be sleeping in their comfortable beds
and the poor under the bridges. (I think she thought
this a cogent argument against egalitarian taxes.)”
Samuelson (1968, 11-12)
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
8

9. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
“Now, Paul Samuelson, aged 20 a hundred years later,
was not Harriet Martineau or even David Ricardo; but
as an equilibrium theorist he naturally tended to think
of models in which things settle down to a unique
position independently of initial conditions. Technically
speaking, we theorists hoped not to introduce
hysteresis phenomena into our model, as the Bible
does when it says “We pass this way only once“ and, in
so saying, takes the subject out of the realm of
science into the realm of genuine history.
Specifically, we did not build into the Walrasian system
the Christian names of particular individuals, because
we thought that the general distribution of income
between social classes, not being critically sensitive to
initial conditions, would emerge in a determinate way
from our equilibrium analysis.”
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
9

10. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
In 1968, MIT Professor and later Nobel
Prize winner Paul Samuelson wrote that
in their quest to provide a hard scientific
basis for the economics discipline
modern economists must believe in a
‚unique long run equilibrium [i.e., an
inevitable outcome for the economy]
independent of the initial conditions’.
Davidson (1996, 65)
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
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11. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Indeed, Samuelson (1969, p. 184) has
made the acceptance of the „ergodic
hypothesis“ the sine qua non of the
scientific method in economics.
[Samuelson (1969, p. 184) indicated that
he used the term ergodic „by analogy to
the use of this term in [19th century]
statistical mechanics“ in order to remove
economics from the „realm of genuine
history,“ and keep it in the „realm of
science.“]
Davidson (2006,11)
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
11

12. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
“Now, Paul Samuelson, aged 20 a hundred years
later, was not Harriet Martineau or even David Ricardo;
but as an equilibrium theorist he naturally tended to
think of models in which things settle down to a unique
position independently of initial conditions. Technically
speaking, we theorists hoped not to introduce
hysteresis phenomena into our model, as the Bible
does when it says “We pass this way only once“ and, in
so saying, takes the subject out of the realm of
science into the realm of genuine history.“
… ‘having once been a jackass’ ...
“What Classical and Neoclassical Monetary Theory
Really was” (1968), Paul Samuelson (1915-2009)
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
12

13. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Uncertainty and ergodicity
Davidson has often stressed (fundamental/true)
uncertainty in his writings. However, there are ergodic
systems which are completely deterministic but do not
allow predictions to be made. These chaotic systems
are part of the real world!
While terms like "ergodic", "stationary", "conservative",
"predictable" or "deterministic" have natural language
meanings, they are also overloaded from dynamical
systems theory and practice where their meanings are
most definitely not coterminous.
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
13

14. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Uncertainty and ergodicity
We believe that a different term should be used to
describe the ‘non-predictability of the future’ that is
compatible with un-/certain but also compatible with
non-/ergodic.
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
14

15. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Stochastic (and non-stochastic):
1660s, "pertaining to conjecture," from Greek
stokhastikos "able to guess, conjecturing," from
stokhazesthai "to guess, aim at, conjecture," from
stokhos "a guess, aim, target, mark," literally "pointed
stick set up for archers to shoot at," from PIE *stogh-,
variant of root *stegh- "to stick, prick; pointed" (see
sting (v.)). The sense of "randomly determined" is from
1934, from German stochastik (1917).
Online Etymology Dictionary
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
15

16. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
“Speaking of randomness in the ordinary sense of this
word, we mean those phenomena in which we do not
find regularities allowing us to predict their behavior.
Generally speaking, there are no reasons to assume that
random in this sense phenomena are subject to some
probabilistic laws. Hence, it is necessary to distinguish
between randomness in this broad sense and stochastic
randomness (which is the subject of probability theory).”
Kolmogorov (1983, first paragraph)
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
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17. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Davidson (2007, 102):
‚In a wider sense, however, ergodicity means the
presumption of a preprogrammed stable, conservative
system where the past, present, and future reality are
predetermined whether the system is stochastic or
not.’
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
17

18. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Davidson (2007, 102):
‚In a wider sense, however, ergodicity means the
presumption of a preprogrammed stable, conservative
system where the past, present, and future reality are
predetermined whether the system is stochastic or
not.’
“When I use a word,” Humpty Dumpty said in rather a scornful tone,
“it means just what I choose it to mean — neither more nor less.”
“The question is,” said Alice, “whether you can make words mean so many different things.”
“The question is,” said Humpty Dumpty, “which is to be master—that's all.”
Lewis Carroll (1797: Through the looking glass)
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
18

19. Here’s the master: Keynes (1921, 23):
©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
19

20. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Keynes (1921, 23):
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
20

21. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Keynes (1921): probability of future events not enough
to understand today’s prices!
Demand for insurance (CDS, …) depends on ‘beauty
contest’ (Keynes, GT) and this situation is one of
reflexivity (Soros).
AIG mattered, underwrote CDS market and got prices
wrong when ‘specially large demand’ arose!
In our terms: markets are described by non-stochastic
processes!
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
21

22. ©
2014
Dirk
Ehnts
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
Book-making deals with non-stochastic randomness
(or uncertainty, etc.) – to ‘protect the book’ is of utmost
importance!
Even in the case of fundamental uncertainty in the
sense of Keynes and Davidson, it still makes sense to
‘protect the book’.
Failures on a systemic level will be solved on a
systemic level, hence individuals do not prepare for
them! (citi’s Chuck Prince: “as long as the music is
playing, you’ve got to get up and dance”)
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
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23. ©
2014
Dirk
Ehnts
„Missouri,
Missouri.
Well,
well,
well,
everything
is
so
uncertain.“
– Mark
Twain,
The
Gilded
Age
September
26th
2014
Samuelson
and
Davidson
on
ergodicity:
a
reformula>on
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